Yes!
It might be related to force quit, but only apple knows. I actually found a note from myelf in my code from years ago - apparently this behavior was introduced in macOS 12.3 
That worked fine!
I'll have to JSON-configure my hyper-⎋ shortcuts, but I can live with that.
Hmm, it's flakey. It works, but the second time I press the keys, it doesn't. If I restart BTT, it works again.
My guess is that BTT still gets confused by the ⎋ up without a corresponding down, and somehow leaves the ⎋ in limbo.
My ⎋ to ⌃C iTerm-specific shortcut also stops working after I press Hyper+⎋.