feat(gamepad): controller discovery + client-negotiated pad type + rich DualSense end to end

The Apple client grows full gamepad support and punktfunk/1 learns to negotiate
the virtual pad type:

- Protocol: Hello carries a GamepadPref byte (offset 21, the same trailing-byte
  back-compat pattern as the compositor; echoed resolved in Welcome at 54).
  Host precedence: explicit client choice > PUNKTFUNK_GAMEPAD env > Xbox 360,
  DualSense (UHID) only where available. ABI: punktfunk_connect_ex2 +
  punktfunk_connection_gamepad (connect_ex delegates; ABI_VERSION stays 2 — the
  trailing byte IS the compat mechanism). punktfunk-client-rs gets --gamepad.

- Swift client: GamepadManager (app-lifetime discovery + selection — Settings
  lists every controller with capabilities/battery/"In use"; exactly ONE pad
  forwards as pad 0, auto = most recently connected, or pinned), GamepadCapture
  (snapshot-diff button/axis events, DualSense touchpad + ~250 Hz motion on the
  rich-input plane, held state released on switch/deactivate/stop),
  GamepadFeedback (rumble → CoreHaptics per-handle engines; lightbar →
  GCDeviceLight; player LEDs → playerIndex; adaptive-trigger blocks → the
  table-driven DualSenseTriggerEffect parser → GCDualSenseAdaptiveTrigger,
  exact for the 10-zone positional modes). The pad type auto-resolves from the
  physical controller at connect time, user-overridable in Settings.

- Host DualSense fixes surfaced by adversarial review against hid-playstation /
  SDL / Nielk1 ground truth: input-report sensor/touch offsets were off by one
  (the kernel read garbage motion + phantom touches), the L2/R2 trigger blocks
  were swapped (the report is right-trigger-first), feedback now gates on the
  report's valid-flags (a plain rumble write no longer blanks lightbar/
  triggers), and the touchpad rescale clamps to the advertised ABS_MT extents.

- Tests: Hello/Welcome trailing-byte back-compat, pick_gamepad precedence,
  byte-exact input-report layout, valid-flag gating, per-mode trigger-parser
  table (incl. packed 3-bit zones), wire conversions, and a scripted loopback
  feedback burst (PUNKTFUNK_TEST_FEEDBACK=1) asserted through the xcframework
  on the rumble + HID-output planes.

Validated: cargo test/clippy/fmt green on macOS + Linux (61 host tests), swift
build/test green, test-loopback.sh green, tvOS/iOS targets compile. DualSense
motion sign/scale is derived from the calibration blob, not yet live-verified
(constants isolated in GamepadWire).

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

clients/apple/Sources/PunktfunkClient/ContentView.swift

@@ -24,6 +24,7 @@ struct ContentView: View {
     @AppStorage("punktfunk.height") private var height = 1080
     @AppStorage("punktfunk.hz") private var hz = 60
     @AppStorage("punktfunk.compositor") private var compositor = 0
+    @AppStorage("punktfunk.gamepadType") private var gamepadType = 0
     @State private var showAddHost = false
     @State private var pairingTarget: StoredHost?
     #if !os(macOS)
@@ -383,12 +384,17 @@ struct ContentView: View {
     }
 
     private func connect(_ host: StoredHost) {
+        // The gamepad-type setting resolves NOW (Automatic → match the active physical
+        // controller): the host's virtual pad backend is fixed per session.
         model.connect(
             to: host,
             width: UInt32(clamping: width), height: UInt32(clamping: height),
             hz: UInt32(clamping: hz),
             compositor: PunktfunkConnection.Compositor(
-                rawValue: UInt32(clamping: compositor)) ?? .auto)
+                rawValue: UInt32(clamping: compositor)) ?? .auto,
+            gamepad: GamepadManager.shared.resolveType(
+                setting: PunktfunkConnection.GamepadType(
+                    rawValue: UInt32(clamping: gamepadType)) ?? .auto))
     }
 
     // MARK: - Trust on first use
@@ -525,7 +531,8 @@ struct ContentView: View {
     /// PUNKTFUNK_AUTOCONNECT=host[:port] connects immediately (trust-on-first-use,
     /// auto-confirmed — dev only) at the saved or PUNKTFUNK_MODE=WxHxHz mode, without
     /// touching the saved host list. PUNKTFUNK_COMPOSITOR=kwin|gamescope|… overrides the
-    /// compositor preference (same names as the host env knob). (IPv4/hostname only.)
+    /// compositor preference and PUNKTFUNK_REMOTE_GAMEPAD=xbox360|dualsense the virtual
+    /// pad type (same names as the host env knobs). (IPv4/hostname only.)
     private func autoConnectIfAsked() {
         guard let target = ProcessInfo.processInfo.environment["PUNKTFUNK_AUTOCONNECT"],
               !target.isEmpty, model.phase == .idle
@@ -547,11 +554,19 @@ struct ContentView: View {
            let c = PunktfunkConnection.Compositor(name: name) {
             pref = c
         }
+        var pad = GamepadManager.shared.resolveType(
+            setting: PunktfunkConnection.GamepadType(
+                rawValue: UInt32(clamping: gamepadType)) ?? .auto)
+        if let name = ProcessInfo.processInfo.environment["PUNKTFUNK_REMOTE_GAMEPAD"],
+           let g = PunktfunkConnection.GamepadType(name: name) {
+            pad = g
+        }
         model.connect(
             to: host,
             width: UInt32(clamping: width), height: UInt32(clamping: height),
             hz: UInt32(clamping: hz),
             compositor: pref,
+            gamepad: pad,
             autoTrust: true)
     }
 }