I never updated a gpus firmeware and neither on the arch wiki or anywhere else did i find info about that. The only thing i know is that the propriatary Nvidia and the Nouveau drivers ship with firmware blobs for parts of the gpu. The tool “fwupdmgr” does detect my nvidia card but also has no updates for it.
But i think it is more likely software related. I cant imagine a hardware failure could make windows partially transparent (tho that could just be lacking imagination).
Timeshift is great for getting your system back after a major fuckup. But i dont think it works as a backup solution that can be transplanted to other systems, but i never tried.
I use Kup to backup my important stuff. It comes with a kcm that integrates into KDEs settings menu and can do automated timed backups. Its a wrapper for bup. It also does Incremental backups.