The chime went silent after you installed the camera

Almost always the doorbell is working and the chime is being told to stay quiet, or is not being given enough to work with. Check these in order; the first one costs nothing and fixes it more often than the rest combined.

The app is set to the wrong chime type

Every one of these cameras asks whether your indoor chime is mechanical or digital, and it drives the hardware differently depending on the answer. A mechanical chime told it is digital will sit silent. If you did not deliberately set this, it was guessed. Set it correctly and test again before touching a wire.

The in-app chime is switched off

Separately from the type, there is usually a toggle for whether the indoor chime rings at all, and some setup flows leave it off. It is a different setting from notifications, and it is easy to miss because the phone alert still works.

There is not enough power to throw the solenoid

A mechanical chime is an electromagnet knocking a metal bar. That takes a real slug of current, and if the transformer is marginal the camera will happily boot while never having enough left over to ring the bell. Check the transformer rating against the requirements for your model.

Your model is not meant to drive that chime at all

Some newer models are incompatible with an existing in-home chime and expect a separate plug-in chime instead. Ring lists the Wired Doorbell 4K Pro (except on PoE) and the Wired Doorbell 2K Plus in that group. If yours is one of them, no amount of wiring will make the hallway chime work.