fix(ios): keep background music playing during remote sessions (#16660)

Configure the iOS audio session with the ambient category so remote
playback mixes with other apps while respecting Silent mode and lock.
Log configuration errors and leave audio activation to playback.

Signed-off-by: Rafal <mrsikorarafal@gmail.com>

flutter/ios/Runner/AppDelegate.swift

@@ -1,5 +1,6 @@
 import UIKit
 import Flutter
+import AVFoundation
 
 @main
 @objc class AppDelegate: FlutterAppDelegate {
@@ -8,6 +9,12 @@ import Flutter
     didFinishLaunchingWithOptions launchOptions: [UIApplication.LaunchOptionsKey: Any]?
   ) -> Bool {
     GeneratedPluginRegistrant.register(with: self)
+    do {
+      // Mix remote audio with other apps while still respecting silent mode.
+      try AVAudioSession.sharedInstance().setCategory(.ambient)
+    } catch {
+      NSLog("Failed to configure audio mixing: %@", error.localizedDescription)
+    }
     dummyMethodToEnforceBundling();
     return super.application(application, didFinishLaunchingWithOptions: launchOptions)
   }