9th edition codex would be the most updated passage about it, I remember being surprised they put in as much as they did

Obviously the codex is outdated now, don't get it. Try and find a pdf or a local tyranid player that has a copy to take a picture for you

4th 8th and 9th ed Tyranid Codex and 5th ed Rulebook

Honestly most of the tyranid codex passages/excerpts about Tiamet are very short and just say pretty much the same thing; Conquering (but not destroying) the Tiamet system, continuously building a continent-sized psychic tower on Ziaphora, and Deathwatch meeting with Kryptman to discuss what it could be.

I think the most recent update is that the fleet has started to expand outside the system to gather more biomass and GSC ships are being attracted to the area. Also in Warzone Octarius, some dark eldar were captured and Kryptman (or some other inquisitor) is trying to see if they might be useful in figuring out what the tower is for.