Time Machine after migration

I have a Mac M1 and I have just did a clean install of Monterey, it wen smoothly. However, when I tried to setup the Time Machine to retrieve the backups from the old install, the computer can see the disk but it cannot "see" the Backup file that is there. If I enter Time Machine, it does not show me anything other than today. I believe it may be due to some involuntary name change, but I can't say for sure. Can someone point me the way to do the adjustments to recover the backups I had there?

Thanks in advance.