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?

If you recently reset your Firefox password, your bookmarks, extensions, and saved accounts won’t sync because Firefox encrypts that data with your old password. Unfortunately, resetting the password erases the synced data for security reasons.

However, you can check if any local backup files are still available on your Parrot OS. Navigate to the profile folder by going to: /home/your-username/.mozilla/firefox/ Look for a folder ending in .default-release or something similar. If you find a file named places.sqlite or a folder called bookmarkbackups, you can restore your bookmarks from there.

To restore them:

In Firefox, go to Bookmarks > Manage Bookmarks. Click on Import and Backup > Restore and select a file from the list. If you used Firefox Sync and have another device connected to the same account, you might still have the data there.