DIAGNOSIS Dirt, moisture, or debris has gotten behind the plastic button cap and is interfering with the physical micro-switch underneath. This is a physical, not electronic, problem.
FIX Power down the device by removing the Quick Release battery pack. Gently pry off the plastic button cap. It's designed to be removable. You'll see the small white micro-switch underneath. Use a can of compressed air (like for keyboards) to blast any dust or grit out of the switch housing. Then, press the micro-switch a few times with your finger to feel the click. Reattach the button cap.
IF THAT DIDN'T WORK If the micro-switch itself feels broken or doesn't click, the internal component has failed. You'll need to contact Ring Support. The Doorbell 4 has a one-year warranty, and this is a known issue they often address with a replacement.
HEADS UP When you reattach the button cap, make sure it's oriented correctly—the word "Ring" should be right-side up. It only fits one way. Forcing it can damage the plastic tabs.