Correcting myself: It appears that many modern client devices (at least current Networkmanager in linux, iphones, and grapheneos) have a "hidden" flag on saved SSIDs and only probe for hidden ones, so the ancestor post is correct for a least these devices.

Older and less sophicated clients, -- that don't explicitly have a 'hidden flag' for saved SSIDs will probe continually for all SSIDs they know.