Time Machine backups failing when studio display is put to sleep / FindMy also not working while display asleep

Since upgrading my iMac 27" Intel to Mac Mini M4 Pro, Time Machine backups are failing when I put the connected Studio Display 27" to sleep. Once the Mac is unlocked and display is on as normal, Time Machine backups recommence from the failed state. (Time Machine couldn't complete the backup to

"5TB_LaCie_TimeMachine". Time Machine did not finish backing up because some files were unavailable.

Backups will resume when your Mac is unlocked.)

Probably also related to this, FindMy won't update location of Mac Mini when display is asleep. Hours go by, and no location for xx number of hours.

Again, once Mac Mini is unlocked (via Apple Watch or Password or TouchID), FindMy location is suddenly updated as normal.

Mac is set not to power down or nap, Energy is on Automatic (but I've tried High Power, no difference), I've selected Prevent Automatic Sleeping When Display if Off. No difference.

Any suggestions? It's driving me nuts.

Must be a config setting somewhere which is preventing both TimeMachine backups & FindMy from functioning proplery.