Input: SDL3 gamepad backend with XInput fallback

Implements issue #14. A dedicated thread owns SDL3 (3.4.16, statically
linked via sdl3 =0.20.0) and publishes per-slot snapshots re-expressed as
the XInput-shaped XboxState, so the TU3 conversion in skate-core is
unchanged. Conversions are exact for XInput-backed pads (stick Y via
bitwise NOT, trigger round-to-nearest). SKATE3_INPUT=xinput selects the
original transport, which is also the fallback if SDL fails to start.
Optional settings/controller.json maps paddles to XInput buttons.

Build: scripts/Ensure-CMake.ps1 locates CMake (PATH or Visual Studio's
copy) for the SDL source build. sdl3-sys is vendored with a build.rs
patch setting CMAKE_MSVC_RUNTIME_LIBRARY from crt-static, because SDL's
CMake (policy CMP0091) ignores cmake-rs' -MT and the static-CRT release
build failed with unresolved __imp_* symbols.

See docs/hails-additions/03-sdl3-gamepad-input.md and vendor/README.md.

docs/hails-additions/03-sdl3-gamepad-input.md

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+# 3. SDL3 gamepad input
+
+Implements upstream issue #14 ("Extending Controller support via SDL Gamepad
+API"), discussed in PR #9. The Windows XInput transport remains available as a
+fallback and for comparison.
+
+## Motivation
+
+- One controller API on every platform instead of XInput on Windows plus a
+  separate backend elsewhere (PR #9 uses gilrs on Linux/macOS).
+- SDL3 supports far more controllers (PlayStation, Switch, generic HID) and
+  exposes features XInput cannot (extra buttons such as back paddles, rumble
+  on triggers, sensors, lights) for future use.
+
+## Design
+
+The gameplay path is unchanged: `skate_core::input::xbox::convert` (the TU3
+conversion with its own dead zone) still receives an XInput-shaped
+`XboxState` with raw values. Only the transport in
+`crates/skate-game/src/input/platform.rs` changes.
+
+- **Threading.** SDL must be pumped on the thread that initialised it, while
+  Bevy runs systems on a pool. A dedicated `sdl-gamepad` thread owns SDL,
+  polls every 1 ms, and publishes a per-slot snapshot behind a mutex; the
+  game reads the latest snapshot each frame, exactly as `XInputGetState`
+  returns the latest state.
+- **Conversion back to XInput shape** (exact for XInput-backed devices):
+  - buttons → XInput `wButtons` bits (`BUTTONS` table);
+  - stick Y: SDL stores `~y` (positive down), so `xinput_y = !sdl_y` restores
+    the original value without overflow at the extremes;
+  - triggers: SDL expands XInput's byte as `b*257` over the full axis, then
+    rescales to `0..=32767`; rounding to nearest (`(v*255 + 16383) / 32767`)
+    returns the original byte for all 256 values.
+- **Packet number** advances only when the state changes, mirroring XInput's
+  `dwPacketNumber`. Device subtype is reported as `XINPUT_DEVSUBTYPE_GAMEPAD`.
+- **Slots.** A new pad takes its SDL player index if that is 0–3 and free
+  (SDL reports the XInput user index there, so the ring light matches),
+  otherwise the first free slot.
+- **Paddles.** Optional `settings\controller.json`,
+  e.g. `{"paddles": {"right1": "a", "left1": "x"}}`, ORs a paddle into an
+  XInput button bit (names in `platform::BUTTON_NAMES`).
+- **Backend selection.** SDL by default. `SKATE3_INPUT=xinput` selects the
+  original XInput transport (Windows), which is also the automatic fallback
+  if SDL fails to start. The backend starts at `Startup` so the first
+  gameplay frame is not stalled.
+- **Diagnostics.** Each connection logs name, SDL gamepad type,
+  vendor/product, paddle availability and SDL driver path, e.g.
+  `Controller 0: SDL gamepad "Xbox One Elite 2 Controller" (XboxOne, vendor 045e product 0b22, paddles not reported, path "XInput#0")`.
+
+## Files
+
+- `crates/skate-game/src/input/platform.rs` — SDL backend, conversions,
+  backend selection, paddle masks, unit tests.
+- `crates/skate-game/src/input.rs` — `start_controllers` startup system
+  (settings + early backend start); log wording.
+- `crates/skate-game/src/app.rs` — comment on why Bevy's `GilrsPlugin` stays
+  disabled.
+- `crates/skate-core/src/input/xbox.rs` — `XboxState` derives
+  `Clone, Copy, Debug, Default, PartialEq, Eq` (snapshots cross threads).
+- `crates/skate-game/Cargo.toml` — `sdl3 = "=0.20.0"` with
+  `build-from-source-static` (SDL 3.4.16, statically linked, no DLL to ship).
+- `scripts/Ensure-CMake.ps1` (new) — finds CMake for the SDL build: uses
+  `cmake` on PATH, else Visual Studio's bundled copy via `vswhere`, and sets
+  `CMAKE`. Dot-sourced by `Build.ps1`, `Build-Release.ps1`,
+  `build-multiplayer-test.ps1`. CI runners already have CMake.
+- `vendor/sdl3-sys/` + root `Cargo.toml` `[patch.crates-io]` + `Cargo.lock` —
+  static C runtime fix, below.
+
+## Static C runtime (release/CI builds)
+
+Release packages, CI and the multiplayer test build with `+crt-static` and
+static Bevy. The first release-style build failed to link:
+
+```
+libsdl3_sys-*.rlib(SDL_stdlib.obj) : error LNK2019: unresolved external symbol __imp_modff ...
+fatal error LNK1120: 16 unresolved externals
+```
+
+cmake-rs passes `-MT` for `crt-static`, but SDL's CMake project enables policy
+CMP0091, which ignores runtime flags in `CMAKE_C_FLAGS` and applies
+`CMAKE_MSVC_RUNTIME_LIBRARY` (default `MultiThreadedDLL`). CMake has no
+environment variable for this, and a `CMAKE_TOOLCHAIN_FILE` environment
+variable would put cmake-rs into cross-compile mode.
+
+Fix: `sdl3-sys` 0.7.1+SDL-3.4.16 is vendored unmodified except `build.rs`,
+which defines `CMAKE_MSVC_RUNTIME_LIBRARY` from `CARGO_CFG_TARGET_FEATURE`
+(`MultiThreaded` with `crt-static`, otherwise `MultiThreadedDLL`; never the
+debug CRT). Documented in `vendor/README.md`. Dropping the patch is possible
+once cmake-rs or sdl3-sys handle CMP0091 themselves.
+
+## Verification
+
+- Unit tests: every trigger byte survives the SDL round trip; stick Y
+  inversion is exact at `i16::MIN/MAX`; paddle masks and button names;
+  existing controller tests (10 total in `input::platform` /
+  `input::controllers`) pass.
+- Dev build (`scripts/Build.ps1`) and release-style build
+  (`+crt-static --no-default-features --target x86_64-pc-windows-msvc`) both
+  link; the static executable imports no `vcruntime140.dll` /
+  `api-ms-win-crt-*`. The dev build's SDL CMake cache shows
+  `MultiThreadedDLL`.
+- In play: Xbox Elite Series 2 over Bluetooth LE detected as
+  `Controller 0 ... ready`; normal skating across several sessions.
+
+## Known limitations / open questions
+
+- **Elite paddles are not reported on Windows** with this setup. SDL picks its
+  XInput driver for the pad ("XInput#0"); the XInput API has no paddles. The
+  hints `SDL_JOYSTICK_GAMEINPUT=1`, `SDL_JOYSTICK_HIDAPI_XBOX(_ONE)=1` and
+  `SDL_JOYSTICK_RAWINPUT=0` made no difference; with `SDL_XINPUT_ENABLED=0`
+  no backend detected the Bluetooth LE pad. The paddle mapping works wherever
+  SDL does report paddles.
+- Controller type is detected but only logged; carrying it into the game (for
+  button prompts, per-model defaults) is future work. Nintendo layouts keep
+  SDL's positional mapping on purpose.
+- Linux/macOS: the backend is platform-neutral but was only built and tested
+  on Windows here.
+- The SDL build adds about 1¾ minutes to a clean build and needs CMake.