Unable to login to my Mac mini post changing home drive?

If you have another macOS admin user account, then you can use the instructions in the following Apple article to attempt to fix things:

Change the name of your macOS user account and home folder - Apple Support

FYI, I highly recommend leaving the home user folder on the boot drive since a simple macOS update patch could break things since you are creating an unsupported configuration. Plus if you are using Time Machine for backups, then you may find yourself unable to perform a restore/migration from the TM backup. This forum has multiple posts where this has happened in the past, especially with macOS 12.x+.

It is better to just store all your large files on an external media data drive. You can relocate large libraries such as Photos, Music, and Videos to external media since Apple actually has official instructions for this setup:

Move your Photos library to save space on your Mac - Apple Support

Change where your music files are stored on Mac - Apple Support

Move your iMovie for Mac library - Apple Support

At this point, I’m not sure what to do except restore from your backup.