Triscendence: No upper limit. :) All Hands adds any number of 3s they can name, but they have to name the number (It can't literally be "infinite.") A common thing in games I run and play is looking at the actual consequences of it in the fiction of the abilities, though. For example: Growth's "I'll cover you" can be used to add 10,000 layers of protective flesh, but that means you've added 10,000 layers of protective flesh. You're going to be big, and different. Even without that, though, the busted/broken feeling you're describing is intended here. (Though, I should say, it's also intended to be not-obvious, and expected that some tables will ignore it if their players aren't doing a close reading of the text.)
All Hands Adjustment: Yes, it counts as an adjustment--All Hands "adds" threes. Triscendence cannot create the effect you're referring to that's received at code U2 -- the U2 ability just "counts" as Triscendence for purposes of its effects. The ability at U2 is intended to be extremely rare prior to further advancement down that track. I could see an argument at a table as you describe about Triscendence leading into U2, but I think that's both unfun and thematically inappropriate, given that Triscendence exposes everything you do to the entire Agency. Maybe that's my actual ruling: sure, you can do it, but you're revealing enough you won't be employed for long.
Thanks for the close reading!! And if you ever need quick responses, we have a great community over at discord.hauntedtable.games that is always talking about stuff like this.
-Caleb