There's also an instrument in this category that could have been built any time in the last ~500y: talkbox bagpipes. While the mouth-blown pipes are probably most familiar, all the mouth is doing is putting air into a bag. Bellows pipes replace this with an arm-operated pump. This opens up an opportunity to point the drones into your mouth so you can manipulate the sound of your accompaniment, turning the drones from a continuous, well, drone, into something lively and danceable. Or, at least, it should. As far as I know no one has built these, and my attempts to convince my bagpipe-maker cousin to work on this haven't been successful.

I was finally successful in convincing my cousin to let me try this, and it does work!

Probably would be slightly better with a louder drone, or by amplifying the drone separately so it can be turned up relative to the chanter.

You'd need to adjust the angles so it could fit in the player's own mouth, and if you want multiple drones it's mildly tricky to get them to terminate in the same place, but this seems very doable. You could also use your tongue to tap drones on and off. Possibly this would even let you switch between dissonant drones, like A and G for an Amix tune?

If you want to play with this, though, be sure you're using bellows pipes. With mouth-blown pipes you'd be risking bagpipe lung.

Update 2023-04-05: another try, with better mics: