Hello gallant205,
Let's start by making sure that your iPhone is all up to date using the steps below:
1. Back up your device using iCloud or your computer.
2. Plug your device into power and connect to the internet with Wi-Fi.
3. Go to Settings > General, then tap Software Update.
4. Choose the software update that you want to install. You can choose to stay on iOS or iPadOS 15 and still get important security updates. Or you can choose the option to upgrade to iOS or iPadOS 16.
5. Tap Install Now. If you see Download and Install instead, tap it to download the update, enter your passcode, then tap Install Now. If you don't know your passcode, learn what to do.
You can also find those steps in this resource: Update your iPhone or iPad - Apple Support Updating should help to further rule out a possible software conflict.
Should that still persist, do you get any response at all when you attempt to adjust the volume buttons on either your iPhone or TV while actively playing a video using AirPlay?
Also, have you had the opportunity to test your iPhone with any other AirPlay compatible devices?
Let us know, and we'll keep moving forward from there.
