Because there is a star named Sol in game's universe. Which makes it more likely TEC's homeworld system than some other star (there is no star named "Sol" in Star Wars). Also there are ship names again as I explain below.
The first 212 star names in SoaSE are actual star names and could have easily been pulled from numerous accessible sources such as Wikipedia (https://en.wikipedia.org/wiki/List_of_proper_names_of_stars_in_alphabetical_order). Many of the other star names as well as planet names are based off of actual people, places, or things. This trend continues with ship names -- you picked up on "Hoshiko" but there are far more obvious ones like "Kodiak". Many of the names have roots with non-English words that are suggestive of the entity -- it's no coincidence that the Ankylon is a tanky titan while the Ankylosaurus was an armored dinosaur. Many other players have made these connections, yet don't jump to the same conclusion that you do. Why?
Well, let us consider two possibilities for this series of coincidences.
The first is that SoaSE really does take place in our "reality". That of course begs the question why there is no planet name of "Earth" or "Terra". Even if Earth was destroyed by the Vasari, that wouldn't explain why there are no references to it in the lore or history of the TEC. In fact, there is not a single reference in the game or the manual to any element of human history or earth beyond the names of entities. There isn't even a casual mention of a year that would align with our calendar or a reference to how the Aluxian Dynasty stemmed from our history. While an absence of evidence is not proof itself, it would be a very odd design decision to frame SoaSE in our own universe without ever once explicitly tying it's lore to our reality.
The second, and far more likely possibility, was stated earlier:
Coming up with a large number of names to use in a fiction universe is quite difficult, and one must accept that the creators of such universe are prone to use our own languages and history as inspiration for their task.
There's a planet in Star Wars called Aquarius, an asteroid called Polis Massa, and a species called the Thalassians. Are we to believe the peoples of the Star Wars universe named a planet after a terran astrology sign and an asteroid "Bread City" in Greek? Could the Thalassians secretly be Greeks from Thalassia or Elves from World of Warcraft? Maybe....or maybe someone just needed a name for a planet, an asteroid, and an obscure species.
Let's try a universe that does have "Sol" and "Earth" in it. There's a race of religious zealots in Galactic Civilizations who call themselves the "Krynn". Did they presumptuously named themselves after the world in Dungeons and Dragons millennia before meeting the human race? Maybe....or maybe someone just needed a name for an alien race.
Most if not all of the Advent capital ship names are Greek, Latin, or Italian words or places -- verbatim. It could be because the Advent are connoisseurs of Classical Western culture....or it could be because designers needed inspiration for names. I think you are reading way too much into the naming scheme of entities in the game. Games aren't immaculate products given to us by the divine, they are made by people who use inspiration from around them to create art and fiction.
Furthermore, you have a tendency to cling to coincidences that support your conclusion and ignore facts that contradict your presupposed notions. Call it hypocrisy, call it confirmation bias -- either way, you are frequently seeing only what you want to see.
And Vasari are obviously not from geographic locations on Earth that some of their ship names might be, but Hoshiko obviously is a word from human language used by humans which isnt main language of the game (except in translations etc) which means its not there as something player can read (otherwise player would have to learn language of game's races to be able to play) but as a name for a ship (optional).
I think Vasari and ADvent if they have any name similarity to real language its only coincidence
Listen to yourself. When the TEC have a ship name that matches a real word, you act like it's a sign from the above, but when the Advent or Vasari have the same thing, you brush it off as just coincidence. You can't have it both ways. We also have a bunch of inconsistencies or misconceptions:
I think "homeworld" *is* supposed to mean as near to origin as you know (aka origin of human species being homeworld of every human, not planet they specificaly were born on).
Your definition is contradicted by the game's lore. The Advent Homeworld is NOT where the Advent originated or evolved, because they were human colonists. General gameplay also contradicts your definition because every capital in the game is considered a homeworld.
There is no reference to any planet as "homeworld" in game (as in playing it) except in other meanings by Advent, this Kol line and Vasari referring to it as something they are trying to get away from.
Check the stats after ending a game, and you will see a stat indicating how many times you built the "Home" planet upgrade, which refers to how many times you changed your capital. The description for the maps "Crossfire", "Desperation", "Nemesis", "Power Struggle", and "Systems of War" all refer to capitals as a "homeworld". In the in-game map designer, the planets frequently used for homeworlds are called "Terran Home" and "Desert Home". Lastly, as a modder I can attest to the fact that the word "Home" is used dozens of times to refer to your capital planet. The game repeatedly and consistently indicates that its usage of "Homeworld" is completely different from your understanding. This is in part why you fail to understand our interpretations of the Kol commander's statement "For the homeworld" -- your usage of the word is not consistent with how the game uses it.
It isnt likely that *everyone* has forgotten something that important. They know about their militant past even though they were at peace for thousands of years. Obviously they have historians, they also remember what they did to Advent for thousand years before Advent reminded them (even if it was kept from public due to nature there must be some recordings).
You are making an assumption because it is convenient for you. Our own history on Earth repeatedly has shown how easy it is to lose knowledge, even if it is important. Whole cities and empires have been completely lost. Technologies have gone through cycles of discovery and re-discovery. We know of monuments and wonders because of their references in ancient literature, yet are unable to find archaeological proof of their existence. The lore may not say the TEC homeworld is lost, but it is certainly plausible. You can't assume one way or the other.
Let's suppose though that the TEC homeworld is still known. That doesn't help your case at all, because that just begs the question even more about why there are absolutely no specific details on the TEC "homeworld". The most reasonable answer is because the designers didn't want to tell you. An open lore can make for better gameplay, and if they don't want you to know the specific name, then that suggests the de facto choice like Earth is incorrect.
In single person analogy, person doesnt forget what town or house they were from even hunderd years later they still know (unless they were
This is a failed analogy. You cannot compare the memory of a single individual to the "memory" of a society where people die and knowledge must be passed on from generation to generation via communication. You are also ignoring the gross difference in time scales -- 100 years is a far cry from the 1000s of years that the game's lore takes place over. We have no idea how old Trader society is, only that the precursors to the Advent were discovered 1000 years ago. How many more 1000s of years of history is there before that? You have no idea, and even if you did know it would be incredibly ignorant of human history to assume that kind of knowledge cannot be lost over such a time scale.
Game played isnt happening from begininng of lore, its after war was already all out for decades and players play on specific parts of game's universe as different faction
Blame bureaucracy. There are some references to goverment not wanting to use too deadly weapons especially in beginning of lore (such as beam cannons). For TEC ofcourse, Advent and Vasari and more than happy to use most unethical things to wipe each other out.
You are missing the point. The purpose of lore is not to dictate gameplay, but to provide setting, depth, and inspiration. The purpose of gameplay is to make a fun experience, and not necessarily to communicate lore. Gameplay and lore are only loosely dependent on each other. If we allowed gameplay to dictate the lore, we would arrive at contradictory conclusions. We know star bases existed before the start of Rebellion, yet why can no one build them at game start? We know the Trade Order had trade ports during the Vasari invasion (you can see them in the intro), yet why do they have to research them again? The reason is simply game design, and no lore explanation is needed.
Those are all obviously factions created from races after they broke up from single goverment to fight more efficiently over multiple fronts (at least I would assume so). Each with their own story behind (Aluxian Resurgence referring to Aluxian dynasty from lore) which hasnt been written yet as part of canon (giving everyone a chance to make their own story about it). For example a single TEC goverment could hardly fight Vasari and ADvent over hunderds of star systems, so by giving authority to every few star systems over all planets and nearby stars (effectively game's "maps") they could fight without having to check in their capital in core worlds for everything while still doing work for them (fighting Vasari and ADvent off), each goverment renaming itself to something else such as Galan Rim Union etc. So did Vasari and Advent for their fronts (Vasari for example can request reinforcements from their main fleet which is still arriving to Trader space through nodes).
They are not obviously anything. You are trying to reconcile elements of the game that are not meant to be reconciled. Not every single element of the game is intended to fit in a single, coherent lore. Some elements exist because the make for a fun game, and are simply inspired by rather than representative of the overall lore. There is no reason to assume an interstellar entity would have to break up in to precisely 10 completely independent factions just to fight a war. The reason for having 30 playable factions instead of just the 6 mentioned in the lore is purely gameplay -- the designers wanted a 10 player maximum with no restrictions on chosen race. You are making things up to reconcile facts that aren't intended to be coherent.
In short, you are frequently finding a story where there is none. Accept that some things in the game aren't intended to speak of the game's lore. They may even contradict the lore in order to preserve the integrity of game's sandbox element.
Let's now go back to the OP:
One of Kol battleship's lines is "For the homeworld" which in TEC's case is obviously Earth. Did something happen to it or are they just saying it for some other reason? Also there are no official systems resembling Sol system and random planet names don't include any planet names from Sol system (but there is star name 'Sol'). As if whole system was wiped out (by Vasari maybe as in rebellion they can destroy planets?).
- It is not obviously earth. Accept that. You don't know if Earth exists in this universe. You don't know because the designers didn't tell you. Maybe in the future they will. But for now, you don't know.
- "Homeworld" could be the TEC Capital. Or it could just be a TEC capital. The lore mentions only 6 factions, yet lets you play as 30. How many factions are there really? You don't know. It's okay not knowing, because that allows you to enjoy your open ended game.
- You don't know why Sol is a star name in this game. It could be because there really is the Sol system in the lore. Or it could just be a name like any other that was chosen because someone had to come up with hundreds of names for a fictional universe. Or it could just be a mistake. You don't know.
I don't know what or where the TEC homeworld is. No one does other than maybe the developers. Even they may not know, because it doesn't matter. That's the whole point of a sandbox game.