That tech increases the bonuses that Precursor Relics give.  So if you have a research relic, it would increase the amount of research that relic generates.  

That's what I think too, but as erischild mentioned, is it actually applied anywhere? In my current game I have three research relics and three economic relics. I get a bonus to research and economy of 90% to each. But after I acquired the research relic bonus via tech trading I still got 90% for both!? I expect an increase to the research bonus, but it is not listed anywhere I looked.

Sorry to say, but that is not correct.  I have Precursor Technologist specialty in my current game.  I have three Research relics with a total of 10 modules.  I have 100% bonus total listed on the resource bar.  This matches the bonus displayed on the planet screen when I hover over Research.  I have 40%, 40%, and 20% listed on the three relics, which matches the number of modules present.  The readouts all calculate to 10% per module, both hovering over the relics themselves and the resource bar icon.  As far as I understand, that is the initial bonus value I always got.  When a display for the Precursor bonuses does get added, I request that it also show up on the planet readouts when I hover over research, wealth, and influence for their percentages.

If a support ticket is needed, let me know.

I have the Ancient trait, which adds bonuses to research for all Relic modules.  I notice that bonus showing up for all the other relics, but not for the Research ones.  This may or may not be a relevant factor.  Who knows?  Maybe Research relics don't actually get research bonuses.

I also do not see any research bonus listed in the resource bar for the Ancient trait and Ascension Crystals.  I do see them in the planet Research hover.

My apolo

My apologies, I misunderstood.  I'll look into getting some additional feedback in for the specialization techs.  

I play the Vulcans as a custom race with the ancient trait. If you have this trait and any relics with a starbase mining them, look on ANY planet under research. You will see you are getting +10% research PER relic mine regardless of type. If i have 3 tiers of an economy relic being mined, my tool tip will tell me that I am getting +30% to both economy and research. 

This is why Ancient is very very OP for a player who can abuse it.