Runtime hygiene: fix RefCounted cycles (clean suite exit), full-length shifts, wand cooldown

- FSM holds owner via WeakRef; ShiftCoordinator is RefCounted (logic-only);
  persistence tests free the Save node -> test suite exits with zero
  'resources still in use' warnings (was ~13) and 57/57 pass
- GameManager uses each scenario's shift_duration_s (900s ~ 10-15 min) for
  real shifts instead of the 300s test duration
- Wand screening gets a 0.8s recharge cooldown with a wand.recharge message
- TODO/DONE/MEMORY/README synced

src/game/game_manager.gd

@@ -64,7 +64,11 @@ var verifier := AccessVerifier.new()
 var wand_screener := WandScreener.new()
 
 var active_scenario_id := "hollywood_building"
-var scenario_duration_s: float = 300.0 # shortened prototype duration for testing
+## Shift length mirrors the scenario default (900s / 10-15 min per PLAN.md) unless
+## overridden for a test or debug build.
+var scenario_duration_s: float = 900.0
+var _wand_cooldown := 0.0
+const WAND_COOLDOWN_S := 0.8
 var scene_root: Node3D = null
 var npcs: Array = []
 var npc_counter := 0
@@ -103,6 +107,7 @@ func _ready() -> void:
 	guard.cleared_target.connect(_on_guard_clear)
 
 	selected_scenario = _build_scenario(active_scenario_id)
+	scenario_duration_s = selected_scenario.shift_duration_s
 	coordinator = ShiftCoordinator.new()
 	coordinator.setup(selected_scenario, scenario_duration_s, 4242)
 	coordinator.npc_spawn_requested.connect(_spawn_npc)
@@ -169,6 +174,7 @@ func restart_shift() -> void:
 	inspector_current_events = []
 	current_incident_active = false
 	current_incident_npc_id = ""
+	scenario_duration_s = selected_scenario.shift_duration_s
 	coordinator.setup(selected_scenario, scenario_duration_s, 4242)
 	coordinator.start()
 	_last_phase = -1
@@ -552,6 +558,9 @@ func _toggle_inspection() -> void:
 ## Handheld wand inspection (The Joke Shop). Only available when the venue
 ## carries a wand. The wand reports an alert; the player interprets it.
 func _toggle_wand_screening() -> void:
+	if _wand_cooldown > 0.0:
+		hud.log(Strings.lookup("wand.recharge"))
+		return
 	if wand_open:
 		hud.hide_wand()
 		hud.set_wand_icon(false)
@@ -615,6 +624,8 @@ func decide_wand(allowed: bool) -> void:
 	controller.screened = true
 	hud.hide_wand()
 	wand_open = false
+	# Short scan cooldown: the wand must “recharge” between guests (PLAN.md: feel).
+	_wand_cooldown = WAND_COOLDOWN_S
 
 func decide_access(allowed: bool) -> void:
 	var controller: Object = _targeted_controller()
@@ -714,6 +725,8 @@ func _close_incident(outcome: String) -> void:
 	current_incident_npc_id = ""
 
 func _physics_process(delta: float) -> void:
+	if _wand_cooldown > 0.0:
+		_wand_cooldown = maxf(0.0, _wand_cooldown - delta)
 	if coordinator == null or not coordinator.running:
 		return
 	coordinator.tick(delta)