I’m seeing the same behavior, but in a slightly different situation.
In our case:
- We do have our own Apple TV and already checked its settings, including “Allow Nearby Devices to Add Users,” and everything looks correct on our box.
- The full‑screen “Join This Apple TV? Add yourself as a new profile on this Apple TV.” prompt appears on multiple iPhones and iPads in our household, all on iOS/iPadOS 26.2.
- The prompt still appears even when our own Apple TV is powered off.
- If we turn Bluetooth OFF on our devices, the pop‑ups stop entirely; when we turn Bluetooth back on, they start again. That strongly suggests a neighbor’s Apple TV in our apartment building is advertising itself and repeatedly triggering the sheet.
Because of this, changing settings only on our own Apple TV is not enough. There doesn’t seem to be any way on iOS/iPadOS to:
- Respect “Automatically AirPlay: Never” for these prompts, or
- Permanently block/ignore a specific nearby Apple TV that doesn’t belong to us.
This makes iPhone and iPad really frustrating to use in a dense apartment environment, since we have to tap the “X” over and over just to unlock our devices.