You aren’t alone, there are a lot of people with this issue that Ring doesn’t seem to want to solve.
I get the notification on my phone and on the history on the app when it sees someone at my front door.
The person presses the doorbell button and it rings outside but it doesn’t ring inside, I don’t get a phone notification and the bell push doesn’t come up in the history on the ring app.
9 times out of 10 mine does this. The button works because it rings outside. The WiFi works because I get a notification to say it’s seen someone at my door. But the button push never comes through. So I’m missing the postman on a daily basis.
I assume your problem is the same as mine? If so, Ring won’t be any help I am afraid. You’ve got to live with it or bin it. They will tell you to uninstall and reinstall the app, reset the doorbell etc etc and then blame your WiFi.