Narrowing down cause why TimeMachine won’t restore emails

Have noticed recently the some Macs can no longer restore individual emails and contacts via ‘Enter TimeMachine’. Trying to triangulate what combination of things leads to this downgrade in features..

There seems to be several variables that could impact things: MacOS version, TimeMachine to direct attach vs. network destination, APFS vs. HFS+ format on the backup drive and whether the drive was adopted from a previous Mac or started fresh.

My local observations say (with “YES” meaning CAN restore individual emails):
Big Sur + direct attach + APFS + fresh = YES
Big Sur + direct attach + HFS + adopted = NO
Monterey + network attach + sparsebundle on APFS + fresh = NO
Monterey + network attach + sparsebundle on HFS + fresh = NO