I like @Omgitstony’s questions. I think we’re assuming the same thing about the ding-dong! sound coming from the doorbell camera unit’s speaker where you have that mounted, but it’s good to have clarification on that point.
I also like that he asked about enabling the chime in the app, because my recollection of installing mine the first time was that the app didn’t prompt for a chime type selection during initial setup. I thought to check it and set it myself (on the app’s Video Doorbell v2 Live Stream screen, tap 
Settings ➜ Chime ➜ Doorbell Chime Type ➜ Mechanical) because I’d installed an Arlo for my sister not long before then and that was part of its setup process.
What, if anything, did you learn by working through the troubleshooting article I linked earlier? Again, I’d probably try adjusting the Chime Type settings as directed before making any more wiring alterations, especially if your doorbell camera unit is getting adequate power, maintaining its Wi-Fi connection, and otherwise functioning as expected.
Mine is also cheap. 
Fortunately it’s still working for me several years on.
I appreciate your taking the time to answer my questions so far, and I look forward to the follow-up.