What happens when the old primary is available and back online?
Synchronous-commit mode and Automatic Failover:
When the former primary replica comes back online, it takes on the secondary role, and the former primary database becomes the secondary database. The new secondary replica quickly resynchronizes the new secondary databases with the corresponding primary databases.
Synchronous-commit mode Planned manual failover:
When the former primary replica comes back online, it takes on the secondary role, and the former primary database becomes the secondary database. The new secondary replica quickly resynchronizes the new secondary databases with the corresponding primary databases.
Asynchronous-commit mode Forced failover:
It transitions to the secondary role, causing the former primary databases to become secondary databases and transition into the SUSPENDED state. It gives you a chance to recover data before resuming synchronization.
Important
Transaction log truncation is delayed on a primary database while any of its secondary databases are suspended (not available to sync). Also, the synchronization health of a synchronous-commit secondary replica cannot transition to HEALTHY as long as any local database remains suspended.
Reference:
• Differences between availability modes for an Always On availability group
• Failover and Failover Modes (Always On Availability Groups)
• How It Works: Always On–When Is My Secondary Failover Ready?
• Perform a Forced Manual Failover of an Always On Availability Group (SQL Server)