First Direct’s app definitely needs re authenticating, you have to ring them.Hmm ... general email passwords (for standard IMAP accounts set up in Apple Mail) should be part of the backup. it's only when using third party apps which have a "device specific password" that need to be set up again.
Oh, and about banking apps ... I guess it depends on the app. Some of mine seem to need me to use my password to log in each time I add/edit/delete a finger print (I use touch-id as my phone doesn't support face-id). So I assume moving to a new phone triggers this too.