I also tried deleting the database again, called update-database and
then add-migration. I ended up with an additional migration that seems
not to change anything (see below)
Based on above details, I think you have done last thing first. If you run Update database before Add-migration, it won’t update the database with your migration schemas. First you need to add the migration and then run update command.
Try them in this order using package manager console.
PM> Enable-migrations //You don't need this as you have already done it
PM> Add-migration Give_it_a_name
PM> Update-database