I've configured Always On AGs for one database on 2019 Standard. It works well. It automatically
fails over to the secondary when I take the primary down.
But there seems to be no auto fail over back to the (original) primary.
I also cannot add a second readable replica.
Is this because this is the Standard Edition, not Enterprise? Thanks
In Standard Edition - you can have one secondary replica and that secondary cannot be set to read-only. It is a limitation of the basic availability group - only a single database and only one secondary.
As for automatic fail-over back to the primary - what are you expecting to happen? If you expect the system to fail back once the primary is back up and available - then no, that won't happen. If you expect the system to fail-over to the now secondary if the primary fails - that should work the same as the original scenario.