Watched those and a few others. In the end, my initial assumption about how these things work was pretty accurate.
Basically, the chime is a 16vac system driven by a transformer. The chime itself (in its simplest form) doesn't do anything until the button is pressed. That shorts the contact from 16vac to the solenoid which causes the "ding". When the button is released, the solenoid releases and swings back the other way hitting the "dong". With a simple mechanical doorbell like this, power is fed at 16vac/10va (typically) directly to the doorbell button so a camera would have no issue using the power provided power to run. The only issue would be when the button is pushed the solenoid could pull too much current and brown out the camera's power so if it has no battery/capacitor to smooth out that 1-2 second button press it might reset.
A more complicated system like one with an intercom doesn't work that way and acts more like a traditional contact/dry switch though it's using 16vac for some reason. The voltage has no available current so it can't run a doorbell camera though it might be able to charge one very slowly should it have a battery. In this case, a separate 16vac transformer is required and the button press must be accomplished via a relay.
In my case, I have a mechanical doorbell (solenoid ding-dong with 3 tones that can play 4 or 8 notes). It also has a rear and side door option which will simply "ding" or "dong" when those are pressed. When I connect my camera up to the side or rear contacts it works fine because it's a effectively a standard mechanical doorbell with a single solenoid. However, when I hook up to the front door, it has a motor with an encoder on the main board. When the button is pressed, the motor spins and the contacts sweep across the different positions causing the 4- or 8-note pattern. The issue seems to be that, much like the intercom style systems, it does not provide enough power to the camera when the motor is running. I can resolve that by using a separate power supply and relay.
However, I am going to see if I can locate a higher power transformer (40va or more) to see if that will provide sufficient current even with the motor running. If not, I'll have to find a way to fit a relay somewhere and probably run wires to the doorbell somehow. If that's the case, I probably won't be using this brand and may opt to go back to the OG Ring unit that worked fine (because it has a battery for wired/wireless usage).
