I recently reinstalled my Linux system

Does that mean you reinstalled over the existing data? Was your home directory on a separate partition? My home and other data are always on different partitions than root. When I reinstall root gets reformatted and home and data just get remounted. If your data is was not backed up or on another device, there is nothing more we can do. https://support.mozilla.org/en-US/kb/ive-lost-my-firefox-sync-account-information

I understand, but usually when I log into my profile, even on another device, my extensions, favorites and even my password are automatically loaded into my profile.

Unfortunately, I forgot my Firefox password, which forced me to reset it to log in.

Sorry, but you did a password reset right?