Fix mouse look swallowing by the HUD

Move guard look handling to the _input stage, recapture the cursor on
window-focus return and when clicking back into gameplay, and make HUD controls
mouse-transparent. Add regression tests for yaw/pitch and HUD mouse filters.
Verified under Xvfb with real relative mouse motion. Headless 237/237, Python
94/94, movement smoke 60 fps.

src/game/guard_controller.gd

@@ -115,14 +115,36 @@ static func _ensure_gamepad_bindings() -> void:
 			press.pressed = false
 			InputMap.action_add_event(action, press)
 
-func _unhandled_input(event: InputEvent) -> void:
+## Mouse look is read at the `_input` stage, before GUI/Control handling. A
+## full-screen HUD or a focused control must never be able to swallow relative
+## mouse motion while the game is in captured mode.
+func _input(event: InputEvent) -> void:
 	if input_locked:
 		return
-	if event is InputEventMouseMotion and Input.get_mouse_mode() == Input.MOUSE_MODE_CAPTURED:
-		rotate_y(-event.relative.x * look_sensitivity)
-		var pitch_sign := 1.0 if invert_y else -1.0
-		head.rotate_x(pitch_sign * event.relative.y * look_sensitivity)
-		head.rotation.x = clampf(head.rotation.x, deg_to_rad(-80.0), deg_to_rad(80.0))
+	if event is InputEventMouseMotion:
+		if Input.get_mouse_mode() != Input.MOUSE_MODE_CAPTURED:
+			return
+		_apply_mouse_look(event.relative)
+		get_viewport().set_input_as_handled()
+	elif event is InputEventMouseButton and event.pressed 			and Input.get_mouse_mode() != Input.MOUSE_MODE_CAPTURED:
+		# Recover capture if the window lost it (alt-tab, compositor focus,
+		# clicking back into the game) without opening the radial menu.
+		Input.set_mouse_mode(Input.MOUSE_MODE_CAPTURED)
+		get_viewport().set_input_as_handled()
+
+## Pure look update, kept separate so the rotation math is testable.
+func _apply_mouse_look(relative: Vector2) -> void:
+	rotate_y(-relative.x * look_sensitivity)
+	var pitch_sign := 1.0 if invert_y else -1.0
+	head.rotate_x(pitch_sign * relative.y * look_sensitivity)
+	head.rotation.x = clampf(head.rotation.x, deg_to_rad(-80.0), deg_to_rad(80.0))
+
+func _notification(what: int) -> void:
+	# A window/compositor focus change can silently release capture. Restore it
+	# when gameplay owns the input layer; menus set input_locked instead.
+	if what == NOTIFICATION_APPLICATION_FOCUS_IN or what == NOTIFICATION_WM_WINDOW_FOCUS_IN:
+		if is_inside_tree() and not input_locked:
+			Input.set_mouse_mode(Input.MOUSE_MODE_CAPTURED)
 
 func _physics_process(_delta: float) -> void:
 	if focus_suppress_s > 0.0:

src/game/ui/hud.gd

@@ -356,6 +356,17 @@ func _init() -> void:
 	debug_label.add_theme_font_size_override("font_size", 11)
 	debug_label.autowrap_mode = TextServer.AUTOWRAP_WORD_SMART
 	add_child(debug_label)
+	_ignore_mouse(self)
+
+## HUD controls are presentation-only. Leaving the full-screen containers on the
+## default MOUSE_FILTER_STOP can swallow mouse motion/buttons before the guard's
+## captured-look input sees them. Make every non-gameplay HUD control inert to
+## the mouse; modal menus are separate CanvasLayers and keep their own filters.
+func _ignore_mouse(node: Node) -> void:
+	for child in node.get_children():
+		if child is Control:
+			(child as Control).mouse_filter = Control.MOUSE_FILTER_IGNORE
+		_ignore_mouse(child)
 
 func set_shift_state(coordinator: Object, scenario: Resource) -> void:
 	top_label.text = scenario.display_name if scenario else "Gig Line"