Setup New Computer from Time Machine Backup Containing Multiple Drives

I prefer to use the Startup Assistant to migrate from the old computer instead of Restoring from the full backup.

I did this a few months ago and had no issues with the external drives I have set to backup along with the Mac.

I don't know what it will attempt to do if you choose the full restore option.

I can't remember what I did, for certain. I think I just told it to use the same drive I had been using.

Since Time Machine can only ever be guaranteed to be a copy of your current drives, I don't try to inherit another backup. I usually just erase the backup and start over. While recently deleted files can be recovered, as soon as Time Machine needs the space, the oldest of those deleted files will be deleted from the backup. It's not archival, so I don't really see a point in inheriting another backup.

However, I don't remember erasing the backup drive, but it wasn't a new computer. The backups have a way of associating with a particular computer, so it may have just kept going. My guess though, is it did a full backup.