I think you need to backup that data using Firefox FAQ backup instructions and then copy them back into the new Firefox setup on the new computer. Sync if it is ever deleted or cleared your sync data will no longer be there to restore back. Sync isn't a backup and once the computer with the data locally saved is gone so will sync as it will no longer have a device to sync back to.

Where is the old computer? Are you signed into your Mozilla account on the old computer? If so, you should then sign into the same account on the new laptop and then you should see data populating the new browser if you have the sync options checked on the old computer. see screenshot

FYI... SYNC IS NOT A DATA BACKUP SERVICE Sync info... https://support.mozilla.org/en-US/kb/how-do-i-set-sync-my-computer https://support.mozilla.org/en-US/kb/how-do-i-choose-what-information-sync-firefox https://www.mozilla.org/en-US/firefox/features/sync/ https://hacks.mozilla.org/2018/11/firefox-sync-privacy/ Sync is not a backup tool but it is a good sync/transfer/move tool https://support.mozilla.org/en-US/forums/contributors/707681