Using 3.4.8033.
If you're not using the Store version, try using the latest 3.5 from the first forum topic. If you're on the Store version there's nothing you can do until a new Store version is released.
I've updated to 3.5 and it hasn't changed anything. But I believe I've fixed the problem for myself.
I forgot to mention that because my laptop doesn't have dedicated media control buttons, I use an AutoHotkey script to rebind Ctrl+Shift+Left to Media_Prev, Ctrl+Shift+Right to Media_Right, and Ctrl+Shift+/ to Media_Play_Pause. I believe these AHK hotkeys send simulated media control presses, but aren't real buttons so alexdo's fix wasn't actually necessary for me. I only thought I needed it because I gave myself the double register bug by having the MusicBee multimedia global hotkeys set to the virtual media control buttons because I must have had the script running when I set them. This caused both MusicBee and Autohotkey to send media control commands simultaneously, instead of MusicBee + keyboard button conflicts other people were having.
I fixed it by changing the MusicBee multimedia global hotkeys to Ctrl+Shift+Left, Right, etc. while the AHK script was disabled. And now after reenabling it everything seems to be working fine including the overlay using the original version of the plugin. Only minor gripe is that as others have reported, audio needs to be played directly through the MusicBee window once after it starts up before the hotkeys begin to register. I noticed the Spotify app doesn't have that problem so I imagine there's a potential fix but who knows? Media Controls do conflict with other media players like Spotify, but that's not a problem for me because I've never needed to have both open at the same time.
Cheers!