I would just like the lock button on the Apple Magic Keyboard to lock the display screen, begin the display screen saver, and depart the show on (if linked to energy), in such a means that I can unlock shortly later routinely utilizing my Apple Watch. Is that this attainable?

It appears to not be, due to a distinction in habits between the Lock Display screen command (from the Apple Menu, or from Scorching Corners Shortcuts) and the habits of the lock button. Particularly I discover this distinction when the laptop computer is closed and linked to an exterior monitor.

After I invoke Lock Display screen (on macOS Sonoma), my display screen saver begins, my show stays energetic, however I have to re-enter my password to unlock the display screen. I am unable to unlock the display screen routinely by way of my Apple watch.

However after I click on the keyboard’s lock button, the display screen saver begins, the show then turns off completely, however then I can unlock it by way of my Apple Watch. So the keyboard’s lock button is doing one thing totally different from the “Lock Display screen” command. It is also totally different from the Sleep command (which could be chosen from the Apple menu).

I do not perceive what is going on on. Is there a setup so the lock button locks the display screen, permits watch unlock, however does not flip off the show?