feat(client): add gauntlet room timer + personal bests (#496)

GauntletHUD in UILayer shows TIMER: MM:SS (PB: MM:SS). Timer starts on
room entry, resets on room change, records personal bests to
user://gauntlet-stats.json. Session summary printed on disconnect.
Hidden in non-gauntlet mode (anti-tedium guard).

Adds room_id and gauntlet_mode fields to GameState, parsed from
ObserverSnapshot. Main.gd wires update_from_state() and finalize().

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

client/scripts/autoloads/game_state.gd

@@ -36,6 +36,10 @@ var current_dialogue: Variant = null  # {npc_name, npc_entity_id, speech, option
 # InputMapper suppresses movement when this is true.
 var dialogue_active: bool = false
 
+# v8 fields (#496): Gauntlet mode — room timer + personal bests
+var room_id: Variant = null  # String room_id from snapshot, null in non-gauntlet mode
+var gauntlet_mode: bool = false  # true when snapshot includes gauntlet_mode flag
+
 # v7 fields (#431, D-059/D-060)
 var pending_recognitions: Array = []  # [{entity_id, x, y, z, remaining_ticks, total_delay_ticks}]
 
@@ -118,6 +122,16 @@ func apply_snapshot(snapshot: Dictionary) -> void:
 	else:
 		pending_recognitions = []
 
+	# v8: gauntlet mode (#496) — room_id and gauntlet_mode
+	if snapshot.has("gauntlet_mode") and snapshot.gauntlet_mode == true:
+		gauntlet_mode = true
+	else:
+		gauntlet_mode = false
+	if snapshot.has("room_id") and snapshot.room_id is String:
+		room_id = snapshot.room_id
+	else:
+		room_id = null
+
 	# v2: visible_tiles with visibility sectors
 	# Derives visible_positions when not explicitly provided (real server mode)
 	if snapshot.has("visible_tiles") and snapshot.visible_tiles is Array and snapshot.visible_tiles.size() > 0: