I have four Wyze Cam v4’s, three with lamp sockets and also experiencing the same issue. I think this has been reported before but still isn’t fixed.
The only way I am able to keep the three lamp socket lights on is exit out of the app after setting them on in the cam’s accessories settings.
Once I go into the app and click one of the individual camera’s feeds, it turns the light off on the lamp socket for that camera. I wish this would get fixed.
It doesn’t seem hard to fix from a developer point of view, the app needs to know to not turn the lamp socket off if it detects that it is on already.