migration made two accounts; which to use?

Migration always creates a new account - when you first set up your computer it will ask if you want to restore from a TM backup or old computer. If you say yes then the account that is migrated will be the only account.

Log into the account that was migrated from the backup and take a look around. Go to system preferences and make sure iCloud is activated. Unless you've created new email accounts between the time you last used that account and now, there should be nothing missing. Your photos and music should be there too. If not you can use TM to grab them but don't use Migration Assistant to do it. See this article: Restore items backed up with Time Machine on Mac - Apple Support

Once you are certain everything you need is in the account that you migrated, you may delete the first account you created.

Modern email keeps mail on the mail server unless you move it. so look to see if the mail appears in read, deleted or archived in the migrated account. If not I can tell you how to move it back to the server

Set up whatever email client you want to use on the migrated account. See, for the most part mail isn’t kept on the computer in a mail application database, it is kept on the server. All that is downloaded to the computer are the subject headers. When you select an email it is quickly downloaded to the computer so you can read it but it isn’t removed from the mail server unless you delete it. Even then it actually gets put into a deleted folder. You actually have to work hard to totally delete email…for the most part.

I have one thought so I hope it’s right. Select the TM Drive‘s icon on the desktop and Get Info. (Comand I). at the bottom of the drive icon there will be a item saying something like ignore ownership. Can’t check my Mac at the moment, on the road with iPad.

For some reason, while you were logged into the account you migrated, the system didn’t think you owned the TM drive. I don’t know if this is an intentional security feature or a quirk. (Apple keeps piling on more security features with every release.) I do know one sure way to avoid it’s happening and how to avoid other potential TM gotchas, but if you are now able to access all your data and applications there’s no reason to consider it. Keep it in mind for your next computer or when a friend asks for help.

When you purchase a new computer the best way to use TimeMachine is to connect your computer or backup drive to the new computer when you are logging into the computer for the first time. At some point it asks if you want to migrate data - answer yes, select the TM drive and save point and let it go. That way there’s a single account migrated and a single account on the computer.

did You access the TM drive by double clicking on its desktop icon or by using TimeMachine (the icon in the menubar)

assuming you haven’t deleted your other account yet, log in and see if you can access TM from there. It isn’t optimal but if so, you can get the files and theN move them to the other account