According to How to update to the new Firefox Sync | Mozilla Support website:
The latest Firefox includes a new version of Sync. Don't want to update right away? No problem. Sync will continue to work as before for now, with one exception.
Signing in to the new Sync is easy to do with a Firefox account. No more pairing codes or recovery keys. Just sign in with your email and password and you're set.
Your old Firefox Sync account will not work for the new version of Firefox Sync, so you need to create a new Firefox Account to use the new version of Firefox Sync. A Firefox Account is required for Mozilla services that require authentication, such as the new version of Firefox Sync and advanced features on Firefox Marketplace like purchasing paid apps, adding app reviews, etc.
You also cannot use Mozilla Persona to login to your Firefox Account.