Here are the planet types that Yor civilization (Synthetic race) can colonize at the start of the game in v3.96.

Aquatic World: Raw Production -50%
Frozen World: Raw Production -50%

Bacterial World: Raw Production +10%, Research +25%, Influence Growth +10%
Barren World: Raw Production +10%, Social Construction +25%, Ship Construction +25%

Toxic World: Requires Atmospheric Cleansing, Raw Production +10%, Research +25%

Radioactive World: Requires Atmospheric Cleansing, Raw Production -50%
Corrosive World: Requires Extreme Colonization, Raw Production -50%

As you can see, there is a bug with Toxic type planets. Synthetic races are said to be able to colonize them directly.
I reported the bug in this post.

Are not the "Adaptable" Ability and the "Synthetic" Race type "duplicate" in this case?

Yes, and it's even worse when the texts in the tooltips, etc. don't match the reality of the game.

If I'm not mistaken, all the bonuses of the "Adaptable" ability are included in the Synthetic race type except the Precursor Archive player wonder. Isn't there another way to give it to the Synthetic races?

The bonus for "Adaptable" Ability in the Galactic Civilizations III wiki.

Can colonize Aquatic, Frozen and Barren worlds.
Enables the Precursor Archive player wonder.

The bonus for Synthetic Race type in the Galactic Civilizations III wiki.

Can immediately colonize Aquatic, Frozen, Bacterial, Barren and Toxic planets.

What I observed during the game v3.96:

Yes, Corrosive World requires Extreme Colonization.

I thought it was the official site, the site is marked as the "Official Galactic Civilizations III Wiki".
Is there another link for the official wiki?

Thank you for the link.
However the site seems outdated.

"Supplied by Starship_Trooper [INFO Racial Abilities, all DLCs v3.01]

Adaptable
+ starts with Extreme Colonization tech
+ gets access to Ultimate Adaptability tech (prereq: Biosphere Perfection)
removes penalties from extreme worlds
gives production bonus to extreme worlds <how much and what exactly?>
+ can build Precursor Archive improvement (Xeno Research)
Research +25%, Level: Research +1% per lvl, Adj: +3 to Research, costs 1 Promethion, one per player"

"Race Type
...
Synthetic
Synthetics are robotic lifeforms that do not require food to survive and can operate in a variety of environments. Unlike squishy organic species, Synthetics fabricate their populations in special factories."