Firefox on Snap is broken. The sandboxing prevents some Firefox extensions from working properly, including the one that allows you to install GNOME Shell extensions from https://extensions.gnome.org (the only official way to install GNOME Shell extensions). They've known about this for years, and still went ahead and removed the option to install Firefox from the APT repositories in Ubuntu 22.04 LTS.

https://bugs.launchpad.net/ubuntu/+source/chromium-browser/+... (The bug also affects snap Chromium, hence the bug title)