Switching to a Vanilla version of the game and reverting back to Fabric (with OkZoomer) resets custom keybinds.

Yeah, thats how controls work sadly :(. Minecraft uses options.txt, which isn't any config format, so unknown options are deleted when reading and rewriting the. Fabric just adds keybinds to the list of stuff to get added to options.txt, and minecraft does it. I really hope mojang switch to options.yml, options.json, options.toml, options.json5, options.hjson, opions.xml, options.cfg, or options.ini (i'd like JSON, but thats just my preference).

How come other mods remember their keybinds?

They don’t? I tested it just for you with ChestTracker, Where Is It and Map Atlases.