Error updating Monterey "An error occurred migrating user data during an install. Reinstall macOS" loop

Hello and welcome to Apple Support Communities, wild-blue-yonder!

We understand you're having trouble with an update on your MacBook Pro. We'd be happy to provide information that may help you resolve this.

Instead of switching out your SSD, try creating a bootable installer to get macOS reinstalled:

How to create a bootable installer for macOS - Apple Support

Please don't hesitate to write back about your results.

Have a great day!

AFAIK, the macOS Monterey installer will only refuse to install with a third party internal SSD the first time Monterey is installed on a particular Mac because the installer has a required system firmware update that must be applied which Apple has required to need the original Apple OEM internal SSD installed (even if installing macOS Monterey to an external drive). Once the system firmware has been updated, you should be able to keep the third party SSD installed internally each time you reinstall macOS Monterey (unless of course the latest installer has a newer required version of the system firmware to install). So far, I have not heard of any reports on these forums about people with third party internal SSDs having issues updating Monterey with each patch (through software update, nor I have heard of anyone having issues with the full installer so far after the first install).

As for the reason the macOS updates have failed to install....have you customized your macOS setup by changing the location of the home user folder or anything like that? Are you running any anti-virus apps, cleaning apps, or third party security software that may be interfering with the normal operation of macOS? You can try booting into Safe Mode to run the macOS update to see if that works --- if so, then you likely have some third party software that is causing a problem.

I have seen a few users on these forums report losing their macOS user accounts after updating/upgrading Monterey (not sure which as people are not clear) so I'm not sure what triggers that condition.

I'm not sure what is going on regarding "migrating user data" during a basic OS update (aka patch).