fix(motion): jump direction, AutoPos cadence, backward/strafe wire & anim

Closes a multi-bug knot in player motion outbound + remote inbound,
discovered via cdb live trace of retail (2026-05-01) and follow-up
visual verification.

Outbound (acdream → ACE):
- JumpAction velocity is BODY-LOCAL, not world (per retail
  CPhysicsObj::get_local_physics_velocity at 0x00512140 + ACE
  Player.HandleActionJump's set_local_velocity call). Was sending
  world; observers saw jump rotated by player yaw.
- Capture get_jump_v_z BEFORE LeaveGround() — the latter resets
  JumpExtent to 0, after which get_jump_v_z returned 0. Was sending
  Z=0 in every JumpAction.
- Backward/strafe-left jumps lost their horizontal velocity because
  LeaveGround → get_state_velocity returns zero for non-canonical
  motion (faithful to retail's FUN_00528960; retail papers over via
  adjust_motion translation, not yet ported). Compute the correct
  body-local launch velocity from input directly and push it back
  into the body so local prediction matches what we send.
- IsRunning HoldKey was gated on `input.Run && input.Forward`, so
  strafe-run and backward-run incorrectly broadcast as walk to
  observers — ACE then animated walk + dead-reckoned at walk speed
  while server position moved at run speed (visible as observer
  lag). Fixed: gate on any active directional axis.
- AutonomousPosition heartbeat 0.2s → 1.0s to match holtburger's
  AUTONOMOUS_POSITION_HEARTBEAT_INTERVAL and the ~1Hz observed in
  retail trace.
- Heartbeat now fires while in-world regardless of motion state
  (matches holtburger + retail's transient_state-based gate, not
  motion-based). Pre-fix the at-rest heartbeat was suppressed.

Inbound (ACE → acdream, remote retail player):
- Remote backward walk arrives as cmd=WalkForward + speed=-1.91
  (retail's adjust_motion'd form). Two bugs were stacking:
  1. AnimationSequencer fast-path returned without updating when
     sign(speedMod) flipped while motion stayed equal — kept playing
     forward at old positive framerate. Fixed: bypass fast-path on
     sign change so the full re-setup runs.
  2. GameWindow clamped negative speedMod to 1.0 when stuffing
     InterpretedState.ForwardSpeed, making get_state_velocity
     produce forward velocity. Fixed: pass speedMod through verbatim
     so the dead-reckoning body translates backward.

Issue #38 filed: 30Hz physics tick produces a chase-camera smoothness
regression at 60+ FPS render. Standard render-time interpolation is
the recommended fix (separate phase).

Findings + comparison vs retail/holtburger:
  docs/research/2026-05-01-retail-motion-trace/findings.md
  docs/research/2026-05-01-retail-motion-trace/fixes.md

TODO: port retail's adjust_motion (FUN_00528010) properly so
get_state_velocity works for all directions natively — would let us
drop the workaround in PlayerMovementController jump path and the
clamp in GameWindow.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

src/AcDream.App/Rendering/GameWindow.cs

@@ -1926,6 +1926,20 @@ public sealed class GameWindow : IDisposable
             Console.WriteLine($"\n=== DUMP_CLOTHING: guid=0x{spawn.Guid:X8} name='{spawn.Name}' setup=0x{setup.Id:X8} APC={animPartChanges.Count} ===");
             foreach (var c in animPartChanges)
                 Console.WriteLine($"  APC part={c.PartIndex:D2} -> gfx=0x{c.NewModelId:X8}");
+
+            // #37: per-spawn palette swaps. The server's clothing pipeline
+            // sends a basePalette + a list of (subPaletteId, offset, length)
+            // triples that splice palette ranges into the rendered character.
+            // We need their IDs to know whether the coat texture's underlying
+            // palette is being overridden by a coat-tone subPalette or left
+            // alone (in which case the texture's DefaultPaletteId — a SKIN
+            // palette — leaks through and the coat ends up neck-colored).
+            Console.WriteLine($"  basePalette=0x{(spawn.BasePaletteId ?? 0):X8} subPalettes={(spawn.SubPalettes?.Count ?? 0)}");
+            if (spawn.SubPalettes is { } subPaletteList)
+            {
+                foreach (var subPal in subPaletteList)
+                    Console.WriteLine($"  SP  id=0x{subPal.SubPaletteId:X8} offset={subPal.Offset} length={subPal.Length}");
+            }
         }
         foreach (var change in animPartChanges)
         {
@@ -2722,7 +2736,14 @@ public sealed class GameWindow : IDisposable
                     // get_state_velocity returns 0 because the gate is
                     // RunForward||WalkForward — body stops moving forward.
                     remoteMot.Motion.InterpretedState.ForwardCommand = fullMotion;
-                    remoteMot.Motion.InterpretedState.ForwardSpeed = speedMod <= 0f ? 1f : speedMod;
+                    // Pass speedMod through verbatim — preserve sign so retail's
+                    // adjust_motion'd backward walk (cmd=WalkForward, spd<0)
+                    // produces backward velocity in get_state_velocity, NOT
+                    // forward. Pre-fix used `<=0 ? 1 : speedMod` which clamped
+                    // negative to 1.0 and made the dead-reckoned body translate
+                    // forward despite the reverse-playback animation — visually
+                    // "still walking forward" from the observer's POV.
+                    remoteMot.Motion.InterpretedState.ForwardSpeed = speedMod;
 
                     if (update.MotionState.IsServerControlledMoveTo
                         && update.MotionState.MoveToPath is { } path)