You can close the prompt, but keep in mind that sync is not a back up service. It's to share across multiple devices. see old screenshot Sooooo many users come here thinking their data is synced or backed up.

To sync you have to login.

Firefox would normally reconnect automatically to Sync on the next start. Make sure that the Firefox Password Manager is working properly as the credentials to login to the Firefox Account are stored in logins.json in the Firefox profile folder.

Using Sync is a possible reason to ask for the Primary Password at startup. This is because the credentials to login to the Sync account are stored in the Password Manager and you need to enter the Primary Password to unlock the passwords and connect/login to the Sync account.