No way to turn off Bluetooth discoverability

Hello, all. I don't understand why it is not possible in Monterey (12.6.1) to turn off Bluetooth discoverability. Am I missing something obvious? There is apparently no setting to turn off discoverability in Bluetooth Advanced, or Sharing.

Listed as "discoverable" (name omitted):

Bluetooth Advanced options:

Sharing options, with Bluetooth Sharing turned off, machine still shown as discoverable:

I got a popup today with a connection request listed only as by MAC address, probably a neighbor. I chose to ignore, but I should be able to control discoverability just as we can with Airdrop, so that I don't receive connection requests at all:

Turning BT off is obviously not an acceptable option when paired devices need to be used. Does this need to be a feature request? Any change in Ventura?