Bricked after attempted OS upgrade.

I would suggest you perform a clean install of macOS by first erasing the whole drive (Intel Macs only) followed by reinstalling macOS & restoring from a backup. Keep in mind erasing the whole drive will destroy all data on that drive so make sure you have a good backup of your important files first.

Since you didn't provide any other information, this is the best I can do to advise you. Knowing the previous version of macOS & the version being installed is helpful (I think you may be installing Catalina and perhaps installed it to the wrong APFS volume since your error message mentions a migration issue). I suspect the hard drive on that older Mac is failing and the OS upgrade just revealed the problem to you since an OS upgrade works a hard drive very hard and will access sections that may not have been accessed for a while.

Here is an Apple article for various startup issues you may encounter:

If your Mac doesn't start up all the way - Apple Support

Without more pertinent details, this is all I can do to assist. You can check to see if an Apple Store or Apple Authorized Service Provider will assist you, or some other local Apple expert since you will need someone who can actually see your setup and exactly what is going on there.

Your Mac is not "bricked" if you can run Recovery. I see it is willing to attempt to re-install Big Sur.

does Disk Utilty says your drive passes First Aid?

is this a MacBook Pro 2103 or 2014 model? what screen size?

what is the date of your most recent backup, and by what method?

What is the exact model of your Mac? You can get this information by entering the system serial number on the check coverage page here (please don't post the serial number on the forum since it is considered personal information):

Check Your Service and Support Coverage - Apple Support

Why were you reinstalling macOS in the first place? Most likely that reason is the same reason for the current failure.

Try running the Apple Diagnostics to see if any hardware issues are detected. Unfortunately the diagnostics rarely detect problems even when a hardware issue is confirmed through other methods.