Based on Mr005K's c.ai Background Image Customizer.
I updated button location, added functionality to store all the images you've used in a library of a sort for quick switching between them.
I used chatgpt to make the changes, so if anyone can do it better, feel free!

Additional note, for me Greasemonkey stopped working on c.ai (on Ubuntu Firefox), so I switched to Tampermonkey. If you're having troubles, you might need to switch too. If it didn't help:

Enable CSP-Bypassing.
Some advanced users have found ways to bypass CSP restrictions, but they require adjusting the about:config settings in Firefox. However, these may reduce security for other sites.
If you’re open to this, navigate to about:config in Firefox and set the following preferences to false:
security.csp.enable
security.csp.enableStrictDynamic
Warning: Disabling CSP can reduce security, as it allows scripts from various sources to execute. Consider re-enabling these settings when you're done testing.

V. 1.1 - Backgrounds are now specific to each char and change dynamically