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/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"