So, to clarify, I'm aware I could dump the database using tools written for the database that don't know anything about azure.
I know I could do an import / export.
And I know I could just extend the point-in-time recovery retention period for the DB.
But what I want is way simpler than that. I don't need to be able to backup to any arbitrary point in time for the last ten years; I just need the normal point-in-time retention period, and the ability to snapshot specific moments (possibly with downtime for a full backup) and have that specific backup stick around after the normal retention period is up.
In AWS I accomplished this with RDS snapshots. I've done a lot of googling and reading through Azure documentation. This seems like a really basic and fundamental feature. It legitimately surprises me that I haven't found it yet, but I'm giving Microsoft the benefit of the doubt and assuming they've implemented the feature, and I've just (somehow) been unable to find it.