This is what I ended up using and it works great. I’m not sure about powering the Sonoff SV from the doorbell transformer since mine was 16vAC and that’s outside the operating range for the SV. I had unused wires on the Cat 5e cable running from the doorbell transformer to the mechanical chime, so I plugged in a 5V phone charger and connected it to two of the unused wires by the doorbell transformer and then connected the 5v to the sonoff sv inside the mechanical chime. I connected the 16vAC to the relay and the wires from the doorbell as a push button. I had to use the PulseTime function in Tasmota so the doorbell would turn on and then off, but it’s working great and there is no noticeable delay from button push to doorbell chime.
I was also able to power an IP camera for the front door using a similar method, Even with the 5v and 16vac on the cat 5e cable I still had extra wires to run 12v from the doorbell transformer all the way to the doorbell. I then added an extra length of wire behind the wall from the camera to the doorbell and tied it to the 12v source. No wires visible and I have all the functionality of a video doorbell, but it’s fully integrated into HA and locally controlled.