Stream/Mirror with AirPods for sound

AirPlay of video with send the audio to the same device (to the Apple TV, and by extension to the TV). You can’t use your iPhone/iPad for audio while AirPlaying video.

You can connect your AirPods, or any other bluetooth speakers, to Apple TV (4th generation or later), and use for sound output (not related to iPhone/iPad audio).

Is AirPlay the only way to Stream?

Is Mirroring done the same way?

AirPlay the only way to stream, mostly. Screen Mirroring is part of AirPlay. Some apps can add other streaming protocols to their own app. The effect is always the same: both video and audio are streamed.

Is there another way to stream video while still using the phone as the sound source?

I don’t understand what you are trying to achieve. Why would you want to use the iPhone speakers for sound output, when using AirPlay? You can connect your AirPods to the Apple TV, and switch back when you’re done.

Please Identify your Apple TV model