How to route audio to AirPods when streaming to Apple TV?

Question

Here's what I attempted

func configureAudioSession() {
    let session = AVAudioSession.sharedInstance()
    do {
        try session.setCategory(.playAndRecord, options: [.mixWithOthers, .allowBluetoothA2DP, .defaultToSpeaker])
        try session.setActive(true)
        print("Session is active. Current route: \(session.currentRoute)")

        if let bluetoothOutput = session.currentRoute.outputs.first(where: { $0.portType == .bluetoothA2DP }) {
            print("Bluetooth A2DP device available: \(bluetoothOutput.portName)")
            // Optionally prompt user or handle routing preferences
        } else {
            print("No Bluetooth A2DP route available; consider manual routing via Control Center.")
        }
        
    } catch {
        print("Failed to configure audio session: \(error)")
    }
}

Essentially, if my iPhone is streaming its audio to a nearby Apple TV, I want my app's audio to go through the pair of AirPods and not Apple TV.

• I don't wanna connect AirPods to the Apple TV
• I tried the above code, but it ended up redirecting the entire system audio to AirPods/Device Built-in speakers. I don't want that -- Instead, I want the system audio to stay streaming to Apple TV while my app can somehow send its audio to AirPods.

I'm open to using private api. Not planning on submitting this to the app store; it's just for a grad school acoustics project we're hacking on.