PSA: Logitech gear might not work after the most recent patch
A few days ago I made a post about my G600 mouse no longer being recognized by SWTOR and only SWTOR. Well, after troubleshooting for a few days and trying a wide variety of thing, I finally discovered where exactly the issue lies.
If Logitech G-hub is on, SWTOR doesn't recognize my mouse and I can only use left and right click. But if I turn off G-hub, then my profile disappears, the DPI becomes stupidly slow, and half my keys become unbound anyway. I don't know if this is unique to the G600 mouse or if it's just an issue between G-hub and SWTOR, but it means that I cannot play anymore.
So now the only solution is to either spend over 100 bucks on a new MMO gaming mouse, wait for the devs to implement a fix, or uninstall the game completely.
Edit: both a workaround and a solution have been found/given in the comments. Thanks to everyone who helped out :)