Time Machine restore doesn't work as described

To enter recovery mode, I hold the power button until the Apple logo appears, select restore from Time Machine backup.

Prompted to re-install Sequoia. OK.

I check in a few minutes, and the computer has booted up as normal, asking for my password.

Everything is as it was.

I need to go back to a previous TM snapshot to fix a major issue with my DAW (music production software)