Hardwired Video Doorbell - App Says Battery

I have just installed a Ring Video Doorbell (2nd Gen). When installing it, I connected the doorbell to the existing wires from the old doorbell. Using a digital multimeter I confirmed that there is 1A, 60Hz, 13.57VAC available at the wires. By touching the wires together I can activate the existing doorbell chime in the house. Furthermore, we've had the old doorbell installed for the last 8 years w/o issue. With the Ring installed I'm having a few issues/questions. First, in the Ring app under the doorbell device health, the Power Source is listed as Battery. The Battery Level is given as 100% (I charged it before installation), but I expected the Power Source to change to Hardwired. I've read a number of places about the trickle charging, but in each of those articles it talks about the Power Source being given has Hardwired and/or showing the lightning bolt in the green battery icon to indicate charging. I'm not seeing any of that. However, I have been watching the live view for quite a while to see if the battery would drain at all and it's not; I'm still at 100% regardless of how much I pester the doorbell. The second issue I'm having is that the Ring system is not activating my existing chime (not the Ring Chime device, but the mechanical chime that's been in the house for... who knows how many years). Anyhow, as I described above, I know the chime still works as I can simply touch the wires together and it sounds off. In the Ring app under the doorbell Device Settings, In-Home Chime Settings, I try to configure the chime. Using Automatic Chime Detection the app asks if I wired the device to a power source. I say "Yes," and the app says the "Ring Doorbell is not receiving power from your doorbell system." I've swapped the wires in the back of the doorbell (though it shouldn't matter); I've cleaned the wires with light-grit sandpaper and isopropyl alcohol and reconnected them - no change. The breaker is turned back on and every other outlet on that circuit is working fine and, indeed, I'm still getting the above described numbers at the wires - 1A, 60Hz, 13.57VAC. I should say too that these numbers are rock solid. I tested them while bending and wiggling the wires and I could not get the numbers to budge at all. So that's where I'm at. I don't know if this is "normal" operation right now - I've read some things on here about firmware suspicions and issues with the iOS app. If anyone has any suggestions or can provide any insight into what I'm seeing, I would very much appreciate it.