This is bazzite specific behavior at this time: it will set the game scope session to use the GPU you pick, but games and Steam will always run on the preferred GPU, IE the DGPU
One thing i'll note, I always shut down. plug in egpu, then boot with it connected. I've had bad experiences trying to hotplug my Core on my old laptop, so I just haven't even tried doing so on my LGo.
I've spent so many days and nights. it is either 7900GRE not fully functioning in AMD Linux driver or @Mister Fluffles 100% set something and forgot what it was