Changing my sound Output Device also changes my Play Sound Effects Through setting - should it?
This is how it’s supposed to work because when you disconnect a Bluetooth sound device, it no longer exists. When that happens everything goes back to the default of Internal Speakers
I just tried it. I had everything set to my headset and when I disconnected it, it no longer showed up as an output device.
There are some apps that remember by output settings so if and when I reconnect my headset it will automatically switch.  It seems that the safety setting is to make sure Notifications always plays and that’s done by the system always setting them back to Internal.
I also checked with my USB speakers by making sound effects go there and as long as those speakers were there even if Bluetooth was connected and disconnected, the notifications didn’t change to Internal.