Backwards Compatibility Vent

So after dropping off and paying to have my fat PS3 internally dusted with new thermal paste and battery mostly so I could play a number of PS2 games on a tv that doesn’t have RCA plugins, I tried to play Prince of Persia: Sands of Time to find the PS3 remote constantly disconnecting from the system. I spent three hours opening and cleaning two PS3 controllers thinking the battery or something else was at issue despite the controller working fine on a demo I played the other day, and alas after much frustration the internet says the backwards compatible ps3 might not be fully compatible with the PS2 lineup. Am I screwed on playing this game? Like what even was the point in cleaning out the console? Yes I have a PS1 library but I play PS2 way more I’m just ticked. I wonder if the cleaning could have caused an issue? I’ve beaten Jak and Daxter on the ps3 prior to the refurbish.