Could my iPhone have connected to a neighbours Apple tv without a passcode?

If you know which neighbor, then you could ask them to change their settings, as “Allowing everyone” could be uncomfortable for them (potentially hearing music that they never selected, or even seeing clips unwanted), depending on their settings.

You can’t prevent it from showing up, as your iPhone is scanning for AirPlay destinations, and their Apple TV is broadcasting that it is an AirPlay destination that accepts incoming connections.

If you see “Connecting…”, then it is still in the process of setting up a streaming connection, but not connected yet. No harm done. They may see the device name (e.g. “Kate’s iPhone”) that is trying to AirPlay (not sure, though). There may come a request for device pairing (a 4 digit code on one device to be entered on the other device), before anything is streamed. There may come a request for a password (if an AirPlay password is set), before anything is streamed.

It is often a good idea (for your neighbor) to set the AirPlay settings on Apple TV to only allow streaming from devices on their own home network. That is usually enough to never connect with unintended neighbor devices.