fix(apple/iOS): immersive streaming — edge-to-edge, no status bar, hidden cursor, native default mode

Streaming on iPad left the status bar up and the video boxed inside the safe areas, on
top of a 16:9 default mode letterboxing on the 4:3 screen, with the iPadOS cursor
hovering over the video. The session view is now immersive on iOS:

- .ignoresSafeArea + .statusBarHidden + .persistentSystemOverlays(.hidden) for the
  session only (home gets its chrome back on disconnect).
- First run seeds the stream mode from the device's native screen
  (UIScreen.nativeBounds + maximumFramesPerSecond) instead of 1920×1080 — verified
  live: a fresh install negotiated the iPad's 2752×2064 with the host. macOS keeps the
  1080p default (a desktop window is not the screen).
- The iPadOS cursor hides while over the video (UIPointerInteraction .hidden(),
  re-resolved on capture toggles) — the host renders its own cursor from our deltas;
  true pointer lock through UIHostingController remains the documented gap.

Found along the way (host-side, not fixed here): at very high modes a keyframe burst
can fill the UDP send buffer and m3 treats the sendmmsg WouldBlock as fatal
("session ended with error: submit_frame: WouldBlock") instead of backpressuring.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

clients/apple/Sources/PunktfunkClient/ContentView.swift

@@ -40,7 +40,10 @@ struct ContentView: View {
                 home
             }
         }
-        .onAppear { autoConnectIfAsked() }
+        .onAppear {
+            seedDefaultModeIfNeeded()
+            autoConnectIfAsked()
+        }
         .onDisappear { model.disconnect() } // window closed mid-session (Cmd+N spawns more)
         // On the outer Group so the sheet survives the trust-prompt → home transition
         // (the "Pair with PIN instead" path disconnects first — the host's accept loop
@@ -77,8 +80,15 @@ struct ContentView: View {
         }
         #if os(macOS)
         .frame(minWidth: 640, minHeight: 360)
-        #endif
         .background(Color.black)
+        #else
+        // Streaming is immersive: edge-to-edge under the status bar and home
+        // indicator, both hidden for the session (they return with the hosts grid).
+        .background(Color.black)
+        .ignoresSafeArea()
+        .statusBarHidden(true)
+        .persistentSystemOverlays(.hidden)
+        #endif
     }
 
     // MARK: - Home (hosts grid)
@@ -243,6 +253,21 @@ struct ContentView: View {
         }
     }
 
+    /// First run on iOS: default the stream mode to this device's native screen so the
+    /// video fills the display instead of letterboxing 1920×1080 onto a 4:3 iPad. (The
+    /// compiled-in AppStorage defaults only apply until any value is saved; macOS keeps
+    /// 1080p — a desktop window is not the screen.)
+    private func seedDefaultModeIfNeeded() {
+        #if os(iOS)
+        let defaults = UserDefaults.standard
+        guard defaults.object(forKey: "punktfunk.width") == nil else { return }
+        let bounds = UIScreen.main.nativeBounds // portrait-oriented pixels
+        defaults.set(Int(max(bounds.width, bounds.height)), forKey: "punktfunk.width")
+        defaults.set(Int(min(bounds.width, bounds.height)), forKey: "punktfunk.height")
+        defaults.set(UIScreen.main.maximumFramesPerSecond, forKey: "punktfunk.hz")
+        #endif
+    }
+
     private func connect(_ host: StoredHost) {
         model.connect(
             to: host,