How can I retrieve files from an old Time Machine backup?

There is a file that is inexplicably missing from my new Mac, and in the TM backups of it. It should be in my Documents folder, which I have residing on / synced to iCloud, but it is not there when I access the folder on iCloud thru a browser, either.

I have had the Documents folder synced to iCloud Drive both on my old Mac and on this new one.

I have searched the Documents folder, the iCloud Drive, and "This Mac."

I have the TM backup from my previous Mac, on an NAS volume. (My current TM for the new Mac is also on that NAS volume.)

How can I get the file from the older TM backup? I tried to add a backup to TM thru Settings, but it looked like it was going to simply make a new backup rather than connect to the old one, so I aborted.

[Re-Titled by Moderator]