fix(client/gamepad): honor an explicit controller type — the per-pad arrival was re-declaring the physical pad

The "Controller type" setting reached the Hello and stopped there. Every pad then
opened with a GamepadArrival carrying its DETECTED kind, and the host builds each
virtual device from that arrival — the session default is only the fallback for a
pad that never declares one. So "emulate my DualSense as a DualShock 4" put a
DualSense on the host the instant the controller connected, and no amount of
reconnecting helped. Apple and the native clients both; Android already applied
the setting per pad.

The setting now rides the declaration too: explicit wins for every slot, Automatic
keeps per-pad detection so a mixed session stays honest. The physical kind still
drives the LOCAL feedback paths — a DualSense emulated as a DualShock 4 keeps its
lightbar and adaptive triggers, and a Deck keeps its rumble keep-alive.

Regressed in 97c67b26 / 76be4c3e (multi-controller support); ships in 0.19.x.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

clients/session/src/main.rs

@@ -204,9 +204,17 @@ mod session_main {
             mode,
             compositor: CompositorPref::from_name(&settings.compositor)
                 .unwrap_or(CompositorPref::Auto),
-            gamepad: match GamepadPref::from_name(&settings.gamepad) {
-                Some(GamepadPref::Auto) | None => gamepad.auto_pref(),
-                Some(explicit) => explicit,
+            gamepad: {
+                // The setting AS CHOSEN goes to the pad service too, not just the Hello: the host
+                // builds each virtual pad from that pad's arrival and only falls back to this
+                // session default for a pad that never declares one, so an explicit choice that
+                // stopped here would be undone the moment a controller connected.
+                let chosen = GamepadPref::from_name(&settings.gamepad).unwrap_or(GamepadPref::Auto);
+                gamepad.set_kind_override(chosen);
+                match chosen {
+                    GamepadPref::Auto => gamepad.auto_pref(),
+                    explicit => explicit,
+                }
             },
             bitrate_kbps: settings.bitrate_kbps,
             audio_channels: settings.audio_channels,