After looking around, you might be facing an issue with Flatpak permissions. Here's a comment I found on Reddit created by u/avamk where they solved the same issue.
All right, after much trying I installed Flatseal and enabled the Firefox Flatpak's access to my home folder.
After this, it created the expected profile folder under ~/.mozilla/firefox/. I put my custom userChrome.css into that profile folder, and >enabled it in my about:config under toolkit.legacyUserProfileCustomizations.stylesheets per these instructions.
With all of these, the custom userChrome.css is finally working!
Link to original post: https://libreddit.tiekoetter.com/r/firefox/comments/rq40cj/cant_find_profile_folder_for_firefox_flatpak_on/
Whoops, you found me. :P