Hello Matthias_Daniels,
It sounds like your iPhone works normally when making a FaceTime call but when you swipe up to go to your home screen while on a FaceTime your video gets paused but the person you're on a call with can still see your video.
If we have misunderstood you or haven't captured the issue completely please feel free to correct us.
If we have understood you correctly, we recommend you try the following:
- Go to Settings > General > Picture iPicture > toggle "Start PiP Automatically" off, restart the device and toggle it back on.
- If the recommendation above didn't resolve the issue, we recommend you try the guidance in: Return iPhone settings to their defaults. Please note: "If you want to save your settings, back up iPhone before returning them to their defaults. For example, if you’re trying to solve a problem but returning settings to their defaults doesn’t help, you might want to restore your previous settings from a backup."
- We also always recommend keeping your devices updated as this ensures optimal performance capabilities and iOS 14.0.1 was just released: Update your iPhone, iPad, or iPod touch.
Please feel free to keep us updated on your progress. Be well!