Failover multiple Basic Availability Groups
This is a difficult scenario to truly handle. I would probably start with running a job on your secondary replica that checks the state of all the databases, and should it become primary for one of them then performs the ALTER AVAILABILITY GROUP [AG] FAILOVER; command for all of the others.

The biggest challenge with this is also running jobs on the primary, and taking care to not accidentally try to fail one of those databases back. You could manage this by checking the AlwaysOn extended event session and looking for failovers there, and do not do work if the database was failed away (as the most recent captured event), this way you don't end up bouncing the databases around all over the place.

You can use sys.fn_hadr_is_primary_replica to check and see if any particular database is the primary on your system.