wrote

That's not how doorbell switches work. There is only one (normally open)
contact with the light across it (there is no "breaking" of the light
contact). When the button is pushed the circuit is closed, causing the
bell
to ring and the light to go out. If the light goes out, the switch is
closed.

Maybe, but it is still not good enough to ring the bell. At least it was in
my case. Replacing the button fixed it. Easy enough to check rather than
the OP insist it is not without doing the simplest check first.