My understanding, as tested by others, is that when you request/click to stream a camera, your phone and the camera do an AUTHENTICATION through the Wyze server (Authentication protocol seems to vary depending on the model and the ODM partner, but most of them use the TUTK protocol), once authentication is approved, they are then permitted to connect with direct P2P. If you are on the same local network, the video stream never leaves the router. If you are on different networks, they still connect P2P, but it obviously goes over the internet in that case.
We even recently had a Wyze employee talking about this just today as it relates to the Floodlight Pros, which are normally 2K:
I don’t know where the scale-down occurs, but if I had to guess, Wyze uses a second alternate stream. I say this because according to public comments elsewhere on here, when Wyze applied to Apple for HomeKit approval a long time ago when all they had was the Wyze Cam V2, Apple denied their application because Apple required a second stream with a minimum resolution that Wyze could not meet on that V2 cam. Wyze cams did support a second stream, but it was not a high enough resolution to meet Apple’s standards, and Apple denied their appeal for an exception. This indicates that Wyze has more than 1 stream, as is common with Smart cameras. So, what is most likely happening, IMO, is that Wyze continues to do cloud uploads and such using the primary stream resolution you have set, but when you stream in a group, they will use the “second stream” at a lower resolution so that the group stream is smooth. Then if you click to open that camera individually, it switches and reconnects back to the higher-resolution primary stream now that it’s not in the group view. So, in this case, the answer to your question is likely that the scale down happens on the camera itself using a second stream that is always scaled down from the primary stream’s higher definition resolution.
But I have to be clear, that I do not represent Wyze and am not speaking for them. I am making the above hypothesis based on general information and testing others have made which suggests this is likely the case. At least, that would be the easiest way to do it since we already know that Wyze cams do support a second simultaneous stream at a lower resolution since this was confirmed when they tried to get Homekit approval so long ago. All the newer cams since the Cam V2 almost definitely meet Apple’s standards now if they ever decide to apply for it again, but that’s irrelevant to the current discussion.
No cloud relay. It is done through the camera. Some cameras can actually even support more than 2 simultaneous streams. In fact, I think the only model limited to 2 streams is the Wyze Cam OG. Most every other model can stream to more than 2 devices at a time.
Incidentally, people have proven that the video stays totally locally if you are on the same network. For example, You can do the following: While on the same local network, start streaming a camera (it does need to authenticate through the Wyze server first). Once it starts streaming, go up to your modem, and disconnect the modem or disconnect the cord going into the modem (the coax cable, DSL cable, Fiber line, etc), while leaving the router on. Your camera stream will keep streaming to your phone/tablet even though internet access is now impossible, proving it is P2P and not relayed. You should be able to do the same thing with multiple streams to prove the same thing. At least several other people in the past have done this to prove everything is local. Granted, Wyze is constantly making changes and security improvements and it’s always possible they might eventually update things to ask the camera to re-authenticate on a set interval to ensure it’s still approved to keep streaming or something, but I don’t believe they have done this yet.
Totally agree. 
It’s hard for anyone to say, conclusively, because there are so many other variables that can affect this. For example, it depends how many other things use your internet and how intensive they are, as well as your use patterns.
What I would do for now, is run a search on “speed test” and pick a site that will test your bandwidth and tell you what it detects as your actual upload availability. From there, you will have a decent idea because you know right now that the camera works fine on 360p resolution, but is not working well on 720p or 1080p. So if you want to be able to do 720p (SD resolution), then you’ll know that it might be best for you to somehow double your bandwidth to be safe. You might be able to get away with doing less than that (for example, maybe other devices on your network all combined use 90% of the upload bandwidth and there’s only a little bit left for your camera to use…so you wouldn’t actually need to double it, you’d just need to double what’s left over and available to the camera currently, which could be way less…hence why it’s complicated to say).
There are some other possible things too. It could be that it turns out that you have sufficient upload bandwidth, but the router that came from your provider is only able to handle a couple of devices at a time, so it FEELS like other devices aren’t working right because the router is too low quality without a good enough processor and RAM in it to handle multiple things at a time (I have seen this too). It’s possible your router might allow you to tell it to give PRIORITY to the Wyze cam and that might make it work better at giving upload bandwidth to the Wyze cam first, but then some of your other devices might not work as well.
There are a ton of other variables that could affect this. I outlined a few examples in the following post:
But for you, I really think it’s mostly a limited bandwidth issue. I’d start with running a speed test. I bet you’re lower than 1.5Mbps if you’re on the lowest DSL. You might only get a few hundred kbps. Feel free to post a screenshot of your upload test.
This is the one I most suggest: https://www.speedtest.net/
It will even give you a link with your test results so you can just share the link result instead of a screenshot.
https://www.speedtest.net/result/15633191474