As you may know (and forgive me if I’m telling you what you already know, many don’t), Setup Assistant is used the first time you turn on your computer and Migration Assistant is used if you’ve already set up the computer and reached the desktop. They are the same process with one significant difference: If you use Setup Assistant your account is created and everything is migrated into that account. If you use Migration Assistant a new account is made and everything is migrated into that account. If you used Migration Assistant you’ll have to log into the newly migrated account to find your stuff.
Now if you use Setup Assistant or you did log into the migrated account and everything is messed up I can suggest two things. First, if you haven’t done so, restart the computer and see if your stuff shows up after logging back in. If that’s no good then something truly did go haywire - that’s rare. I’ve used Migration and Setup Assistant hundreds of times (I’m a tech worker) and I’ve seen only a small handful of total fails. You have two courses of action. Delete the account (you may have to create a new Admin account first, you can’t delete your only account) and try again. That will probably work assuming your TimeMachine (or cloned) backup is good. In very rare cases I’ve had to start completely over, wiping the drive, reinstalling the OS and then using Setup Assistant to restore.