The backup methods is with PC using Firefox FAQ backup methods for profile, bookmark, login/pswd, and maybe history in this process. But if the PC has nothing to sync to there nothing that can be done as the password change and login will clear out what was there and other devices will show the same results as well. You don't have to reset mozilla forum to post to this site. As it seems at this point when you also logged out of those devices and reloged in it clear to match the Desktop Firefox which means any data that was there still is gone now. And if those data where sync from the Desktop those other devices will not have them from the reset and relogged in process as it will match what the Desktop OS Firefox browser had no data to sync from. This is my understanding of using sync. Another is Sync isn't to be used for Backup that's not what it was made for.

Kevin, if your data still exists on the other PC, then I would try to back it up before you run Firefox again on that computer.

This is of course to avoid Firefox syncing and removing the data, if you were to launch it.

See the section "Finding your profile without opening Firefox" here: https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data#w_finding-your-profile-without-opening-firefox

Once you have found the profile folder location, you can copy all profile folders that you find, to be safe.

But again, I wouldn't run Firefox on that other PC unless if you are sure that you have a backup of your profile folder.