I’m having a similar issue for 7 months. My Apple 4k TV pairs with my iPhone but the Apple TV app on my phone doesn’t connect to the tv. I’ve tried everything: restarting both, updating both, removing and reading devices, restoring and still no use. I was hoping apple would fix this in their last two updates for both the iPhone and Apple TV but neither has helped. I have an iPhone 13 so I don’t know why there is any issue with pairing, I wish the previous Apple TV remote app was still available as the latest integrated remote app is very limiting and obviously glitchy. I hope Apple corrects this soon as it’s almost been a year and I’ve been unable to control my Apple TV with my phone, it’s very frustrating when I lose my remote.