Time Machine not showing up in Recovery

[Nimrod7]

I had a Mac Pro 2019 Big Sur 11.2.3, that I backed up with Time Machine.
I am pretty sure that the back was complete.

I am trying to restore that backup via Recovery into a Mac Mini 2018, last holding same Big Sur version.
In recovery I can choose the disk, but after that no backup is showing.

The hierarchy in the Time Machine hard drive seems fine.
Anyone can advice, what I am missing?

 

[Weaselboy]

With Big Sur, Time Machine only backs up the data volume and not the OS. So you will need to install Big Sur on the Mini, then use the backup to import everything during system setup.