HI wmrwl,
How to upgrade Blesta.
First you have to migrate Plesk to plesk migration then you have to login the blesta panel and reissue blesta for the new IP. then upload blesta https://docs.blesta.com/display/user/Upgrading+Blesta
~/admin/upgrade
then If Plesk user password not changes then just replace new plesk IP and admin user paword automated all customers Plesk user password works fine. If your customer user password changes then you have to set password menaully.