I should’ve mentioned this earlier: 
I am not an electrician.
Having said that, I have done a lot of troubleshooting with my own Video Doorbell v2 and Chime Controller and feel pretty comfortable with it, especially since I determined that my home’s mechanical chime had been wired incorrectly before I moved in (so I fixed that to resolve a chime problem I was having, and that’s why I try not to make too many assumptions about existing installations and prefer testing to confirm the wiring).
Regarding the new picture, I imagine somewhere in the home you have a red and a white wire connected together, like with a nut, and that could be anywhere.[1] I think your previous Video Doorbell v2 photo (the one showing the multimeter) showed a red and a white wire coming out of the wall by the door (looks like the red wire insulation is mostly covered in white paint). I suspect that you also have a red and white wire pair connected to the transformer.
What you describe about your Video Doorbell v2 remaining powered when the wires are disconnected (I’m not sure if you mean disconnected from the chime or from the doorbell) and then shutting down makes sense to me, because that unit has a capacitor inside that keeps it powered for about a minute (more or less) once the low-voltage AC is removed.
That’s probably the easiest thing to do, and I wouldn’t blame you for that. It’s not what I would be inclined to do, but I’m stubborn. 
One of the reasons I bought Video Doorbell v2 in the first place was because I was glad that Wyze had finally released a doorbell camera that could use a home’s existing chime, and I wanted to be able to continue using the working chime. If I was in your situation and had confidence that the chime worked, then I’d want to use that with my new doorbell. While I don’t have a Wi-Fi Chime myself, I like the concept and appreciate that it offers some additional flexibility, especially since you can use it with other Wyze Cams. 
If you’re not going to use this existing electronic chime at all (if you’re going to use only the Universal Wi-Fi Chime), then you could probably just connect the chime’s red and white wires together to bypass the chime entirely and merely use your transformer to power the Video Doorbell v2. If you want to use Chime Controller for its fuse capacity, then you could also install that in the circuit, but in order to do that I think you’d still want to know which wire at the chime (red or white) is from the transformer side and which is from the doorbell button side.[2]
I’m not sure what your meter is supposed to be reading in that photo. I see the red probe on the chime’s white wire, but I don’t see the black probe touching anything.
According to the manual I linked in a previous post, batteries are not to be used if the chime in connected to a transformer (the instructions note this in several places), and the SYNC button is only for getting the chime connected to a wireless doorbell button. If you’re installing this with a typical wired doorbell button, you wouldn’t use SYNC at all.
Edit @ 2026-02-26T20:36:41Z
Just as an example of what I’d expect to see in terms of your measured voltage, this is what I see when I test my transformer that’s rated for 16 V AC, 10 VA:
Whenever I’ve measured the voltage at the doorbell button wires, I’ve consistently read in excess of 18 V AC.
It’s also possible that you have three red/white pairs that come together at some location so that several wire nut connections are hooking things up to complete the typical doorbell circuit. ↩︎
See also Can I use Wyze Video Doorbell v2 if my in-house chime is broken? ↩︎