Yesterday (19/08/2023) everything worked fine. Today (20/08/2023) I can no longer login to Twitch using Firefox. I restarted browser and cleared cache. No change.
EDIT: I tried again after 30min and it works again. I have some privacy-oriented plugins but I don't play with custom useragent.
Twitch's official stance is to support the latest two versions of Firefox. Are you modifying your browser agent string at all? Or using any plugins that are privacy/ad-blocking related?