Thanks for posting that single-door version. The only doorbell which comes to mind (for now) which works with a power-supply as well as battery is the new Skybell Trim Plus
The manual shows some terminals on the back that can be connected to a chime, there's no indication that it can be powered this way. It does have a market with people in apartments, but I don't think many others will want a rechargeable doorbell.
Someone pointed this out in another thread, but this doorbell camera is somewhat large.
It would be nice of they made a single door version of this: VTO3211D-P2