I'm using remote control from my smartphone with Google TV (former Google Play movies) app as described here https://www.androidpolice.com/2021/09/27/hands-on-how-to-android-tv-new-remote

It works perfectly fine unless I turn off the Mi Box.

When turned off bluetooth connection becomes unavailable and Mi Box disappears from available devices in the app. So I can turn it on back only using the original remote stick. But why? The original remote stick works via bluetooth also. Means the bluetooth is available indeed.

Normally, when turned off, the icon should become red but bluetooth connection should persist so I can turn on the box back.

I'm struggling with this for some time, already tried different phones, toggling HDMI-CEC (it has no effect in my case, as I'm connected to a monitor, not tv), checked all the app versions but still no luck.

Also, I noticed that when the remote app is connected via Wi-Fi only, after turning off the icon becomes red and the connection persists. But I can't turn it on of course, because on the latest firmware Mi Box can be turned on only via bluetooth. And when I turn on bluetooth you already know what is happening...

Any ideas are appreciated.
My firmware is the latest one Android 9, build 3933.