Magic keyboard OFF switch doesn't work - it stays on

When I turn off my magic keyboard using the physical switch (so, it no longer shows green), nothing happens. The keyboard continues to type just fine. Sometimes, at some point later, it finally disconnects. But not always.

Apple's own documentation implies this is the wrong behavior. It says the switch "turns off" the device.

Other people have been reporting this for years, but none of the threads has had a resolution - lots of bumps and upvotes, no resolution, all threads now closed. So I'll say my piece here. I don't like this for a lot of reasons. For example what if I'm trying to save batteries since it's low and I know I'll need it later? Or what if it's acting up (which is does occasionally) and I need an easy way to reset it?

But even more, I want to trust that when I turn off an Apple device, PARTICULARLY using a hardware switch, it actually, you know, turns off. It just feels bad, like a privacy invasion, or Apple "knowing better" than I do about whether I want my keyboard turned off.

Anyone know if there's a remotely good rationale for what's happening?