I've got a set of Jabra Bluetooth headphones, and I don't see the problem you do with disconnecting my Keychron, but they do like to connect to all my devices at once, but then are only capable of actually listening to one at a time and tend to get "stuck" on whatever the latest thing was to make a noise. Pair that with the fact that notifications exist and often make noise, and I not-infrequently have it switch away from music or YouTube or a video call or whatever to some other device that just made a notification sound, then get stuck on that device.
If you haven't, you might look into power savings settings for your keyboard. You can change some of that stuff with key combos. I'm sure it's documented on the Keychron site, but a lot of it was printed on a card that came with it, too. I had some powersavings-related annoyances that I solved by basically shutting off sleep mode. Battery life's still acceptable, so no big deal (for me—some people might need weeks and weeks on a charge).
The one exception is when I also have BT headphones connected to the MBP and the keyboard idles into disconnecting - for some reason connecting the BT headphones when the keyboard and mouse are already connected is no problem, but connecting the keyboard when the mouse and headphones are already connected almost never works.