Video Doorbell Pro power supply and Plug in Adapter confusion

I have just received a replacement Video Doorbell Pro as my last one had a cracked button and foggy image, presumably due to water ingress. The replacement unit included a Plug-in Adapter (2nd gen) in the box. As the power supply for my previous Doorbell Pro used the 45 year old doorbell house wiring I decided to replace it with the new Plug-in Adapter supplied. This was my first mistake. The new Doorbell Pro did not work with the Plug-in Adapter supplied with it! Dead as a dodo. I thought that the Plug-in Adaptor must be faulty so I connected the new Doorbell to the old wiring and it set up fine. I then discovered why it didn't work. The Plug-in Adapter (2nd gen) is rated at 24v **DC** but the Video Doorbell Pro (1st gen) requires a 16-24v **AC** power supply. This is extremely confusing, especially as the Accessories page on the Ring website states that the Plug-in Adapter (2nd gen) works with the Video Doorbell Pro. **It doesn't.** I am hoping that someone from Ring will read this and be able to clarify or rectify this problem and save other customers from the frustration that I experienced after much time spent routing the cable. I have returned the new Plug-in Adapter (2nd gen) with my old Doorbell as these appear to be in short supply.