Does Bazzite use a gamescope session on wayland by default? Gamescope has a bug which prevents the wayland client from drawing the steam overlay. I suppose it’s unlikely to be the same issue but I happen to be dealing with it on my system (not Bazzite) so I immediately made the connection.
I like tofi as a wayland alternative. Unfortunately like so many of these projects it seems to be somewhat recently unmaintained.