Streaming apps such as netflix or Prime Video cause my video to lose signal

After trying everything from reinstalling apps, resetting the console, checking connections and restarting the device all were unsuccessful. I unplugged the device and left it unplugged for about 10 minutes and now after powering the Xbox back up everything
is working as intended.

I agree with you, when we try to sream a video app (OTT Platform) such as Amazon Prime, Netflix is fine if they block it. But my question is when I'm using a media player app (VLC in my case) which is playing a video from my local disk. So what's wrong if I stream my local video content before starting the game?

I too have been having this issue but is only when watching Prime Video. All other streaming videos, youtube, twitch, netflix work just fine but the controller keeps timing out on Prime. It didnt used to do this so I assume it has something to do with
an Amazon Prime Video app update that happened within the last month or so. The controller shouldnt be timing out with the headphones attached and video playing. If the video is paused for too long it would time out, but only then.

All Prime Video memberships let you stream up to three titles at the same time, but you can only
stream the same title on two devices at a time. Even Netflix's most affordable price plan is about the same as
Amazon Prime Video.

Check each service plan for further info on streaming.

Seems to be the majority of video apps.

Netflix, prime, youtube, bluray