You should be able to connect to Sync using Already have an account? Sign in when you go to use Sign in to Sync in the Menu Panel. Connect another computer to Firefox Sync

You'll need both the email address that you setup Sync with and your account password.

Note: Sync was intended to be used to synchronize data across multiple devices, it wasn't intended as a backup device when reformatting a device. If you have any problem connecting to Sync again [like not remembering your password], do not ask for a new password - the stored data will be wiped from the Sync server when requesting a new password [user data privacy protection].

Earlier I read somewhere on Mozilla only that you backup bookmarks on mozilla servers and if I can't restore from server, then it's of not much use.

Sorry, but as I stated Sync wasn't intended to be a backup service. Whatever you read that told you backup Firefox user data by using Sync was incorrect. It is of "great use" when used properly - to synchronize multiple Firefox installations.

That said, do you or do you not have the username (email address you used to set up Sync initially) and the password for your Sync account? If you have them both, what happens when you try to sign into Sync as the hyperlinked support article explains? If you don't have them both, or you requested a new password when you had a problem logging in to Sync, I hope you learn from your mistakes, because either of those mistakes are "on you".