I’d recommend you to look into “make vertex parent”. In my experience that provides the most reliable parenting to a face (three vertices) or point (one vertex).
You could also use bone constraints for it but it will be iffy since the bone won’t stick to the normal of the face without a lot of trickery (that is never quite 100% robust in my experience anyway).
I haven’t managed to parent a bone to a vertex directly but it should be possible. In my test I’ve used empties as intermediates. The benefit being that you do get some more control because now your bone’s will be following the empties through a copy transform constraint that you can dial up or down or otherwise influence.
Oh this is the solution I was looking for!
The bone was properly controlled by the face’s transform, rotation, and scale.
To do this, unlike Maya, it had to be parented to 3 vertices.
I’m happy to find the answer.
Thank you so much for attaching the video too!