I've not used bazzite before. But I was just thinking you might be having weird issues if steam is installed as a flatpak or some other sandboxed environment.

Here's what I'd try (in order of ease to try):

• switch from Wayland to x.
• ensure steam is natively installed.
• test the open drivers instead of the closed.
• try a different distribution like endeavorOS which is great for gaming.

Test in-between each step and switch back or tweak as desired. You really shouldn't have to spend more money for new hardware unless your GPU is faulty.