How do I disable my in-home mechanical doorbell from chiming every few minutes when the power goes out?

The Power Kit to my Ring Doorbell Elite appears to have died, and now my mechanical doorbell chimes annoyingly every couple of minutes, much like a smoke detector when the battery is low. Because there is no power to the Doorbell, and the Doorbell is set up for Ethernet via the now-dead Power Kit as well (not Wifi), I cannot simply connect to it via the app and disable it since it isn't Wifi enabled (everything goes through the dead Power Kit). How can I turn the mechanical doorbell chime off manually since I cannot connect to the doorbell, and since the Doorbell has no other way to connect to my account?