The new iMacs can only run macOS Big Sur and later, isn't that correct?
That said, is it possible to restore a Time Machine backup created from a Mac running an older version (say, Catalina) onto such a new iMac?
I mean, obviously I'm not trying to get Catalina to run on the new machine, I was just wondering if it's still possible to use Time Machine to get my data off the old backup, given that the OSes don't match.
Strongly suggest only migrate the User Account and nothing else. Although Catalina uses 64 bit Applications and extensions - Big Sur on the M1 Chip is different. Just because an application worked on Catalina does not automatically translate to working on Big Sur and especially on the M1 Apple silicon CPU. Further, software issues that may have been in the Catalina installation if migrated to Big Sur will muck the virgin installation on the Brand New M1. IMHO
Yes, it is possible to set up a new Mac - with an up-to-date macOS - using a backup from an older Mac - with an older version of macOS. Another option would be to use Migration Assistant or Setup Assistant.
Restoring Time Machine backup with old macOS onto a new machine with newer OS?
