Firefox isn't a backup program if you didn't move or copy the data or profile over to the new computer there is nothing that it has to restore. Sync isn't a backup nor does it do backup it sync data between active devices for the profile. You need to sync the old computer or copy the data over to the new computer to get the info and data back.

Did you possibly reset the password of the Sync account because you forgot the password?

Resetting the password for the Firefox Account because you do not remember the password will remove all data stored on the Sync server because this password is used to encrypt your data before it is uploaded to the Sync server and only this password or a possible recovery key can decrypt this data.

Note that you can transfer your personal data directly from the old device to the new device if you still have access to the device.

• https://support.mozilla.org/en-US/kb/recovering-important-data-from-an-old-profile
• https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles