I can’t speak to the Android issue but iOS 16 does not work well with Companion. As far as I know Zwift do not have a fix for it. If the device can run iOS 15 then I suggest downgrading it. Details on this thread.
This action seems typical if your phone going on and off of your WiFi. You might try disabling WiFi assist, or turning off cellular service while using the Companion app, or moving your router closer to your Zwift area.
Not that case for Adroid. I use this setup for leading events 2 times a week, this is new problem. Why game mode returned directly after leaving event? This is Windows app problem, probably Zwift broadcast process fails.