How to restore files from old time machine backup on new Mac mini?

I have a Time Machine backup from my old 2019 imac which is non operational.

i have recently set up a new Mac Mini 4 which has several users. Almost all our data was restored from the cloud brilliantly. I attached a new external drive to the mini and started Time Machine backups. All seem S good

we have found a couple of files that weren’t on the cloud and would like to recover them from the old iMac Time Machine backups.

i don’t seem to be able to see the old backup if I plug it into the mini.

Advice on how to do what I want to do be appreciated.

[Re-Titled by Moderator]