My doorbell buzzes at the same time it ding dongs. It only buzzes as
long as the button is being pushed. What is up?

Nobody Home?

Doorbells do that. You're putting AC current through a coil in
the electromagnet that hauls the "clapper" up when you push
the button. That coil and everything metallic nearby is vibrating
at 60 Hz, or some harmonic of that, because you've got
a magnetic field that's cycling at 60 Hz.

--Goedjn