Assuming that the WAGO connection is good and that the orange wire nut connecting the “common” black wires (I would expect to see 3 of these meeting at that nut) in your chime box is also making a good connection, then your first photo shows what I would expect to see in a 2-doorbell setup for a single mechanical chime. I think that photo is helpful. 
I still don’t know what would cause the Duo Cam Doorbell itself to buzz or hum, though, and I wonder what Wyze Support has to say about that.
Also, because your setup is using a Wyze smart doorbell for the front and a (presumably) “dumb” doorbell button for the rear, another recent topic comes to mind. Since I haven’t seen a clear answer in that case, I wonder if that second doorbell button is part of the problem for you. What happens if you temporarily disconnect that by removing the red wire from the chime’s REAR terminal and test your Duo Cam Doorbell? Does it still make the unwanted noise?