How many Wyze cams are we talking about? Did you previously have them continuously streaming using any other system that pulls RTSP streams continuously?
On the Wyze forums, several people have reported having problems with the RTSP firmware when trying to use more than 3 Wyze cams with RTSP at the same time. Others have no issues. It's not completely clear what the issue is, but the Wyze RTSP firmware seems to interact badly with some mesh routers. Do you have a mesh router?
And yes, there is certainly a limit to how many hosts are going to be able to pull via RTSP from a Wyze camera. I don't remember how many, but the camera is not capable of serving more than a small number of RTSP streams at a time. (Something like 3 or 4 if I remember correctly.)
Any Wyze sign in box that appears automatically is for sign in via the Wyze service, not via RTSP. You get only one sign in prompt for the Wyze service no matter how many cameras you have. After you sign in, you'll be able to select which cameras to stream from.
To use RTSP on Wyze cams, you must add manually using the RTSP urls. It sounds like you already have that part figured out.
For the sign in to the service, if you got the password wrong a few times, Wyze may have locked you out until you create a new password.
Try exactly the following steps:
1. Disable the wyze sign in box using the slider at the top left of the title bar
2. Check with the Wyze app to make sure your password is still working by signing out and back in. You might have to reset it due to the failed attempts earlier. Make sure you can get in with the same credentials you'll try to use.
3. Go to home settings > devices > add camera (green button)
4. Set the type to "Wyze" and click "Add" to sign in
5. Sign in with the credentials you just confirmed are working via the app.
6. If it still doesn't work, use Report Bug from home settings, and check the checkbox to include logs and settings from your device.