Hello Valkontos,
Thank you for reaching out in Apple Support Communities. We understand your unable to connect your iPhone to your Apple TV. We'll be happy to help.
If you haven't tried yet, let's go ahead and unpair your iPhone to the Apple TV. For directions, please follow the section in this article that says, "Unpair your iOS device from your Apple TV": Pair your iOS device or Mac with your Apple TV Then, let's re-pair the iPhone to your Apple TV and see if that helps.
In addition, let's ensure that your iPhone is updated to the latest version of iOS 15.2 and that your Apple TV is updated to tvOS 15.2. Here's two articles on how to perform each step:
- Update your iPhone, iPad, or iPod touch
- Update your Apple TV
We look forward to hearing back from you with an update.
Kind regards.