Removing the old paint “edges”

If your fingers are doing the sanding, its going to continue.
Block it with some 80 grit. Reprime and block your way up to 320/400 wet sanding.400 or 600 is all you need for paint.

If I’m following, the normal process to have more than one coat of primer? I thought (keeping in mind I don’t know) you surface prepped and then primed/painted...

How much profile is needed for paint to adhere? Can you get the primer finish to smooth?