PC3 Phase 2.3: networked play path in the game

- Session autoload: carries {world_id, host, port} from the world browser
  to the game scene.
- world_list.gd "Enter World": POST /api/worlds/{id}/join -> Session.begin
  -> load game.tscn. On 503 (backend has no orchestration) falls back to
  local single-player; other errors surface on the card.
- api_client.gd: join_world().
- game.gd (new, on game.tscn root): local single-player by default; when
  Session.active, connects a NetworkClient to the world's dedicated server
  and runs networked -- forwards the local Player's input each physics
  frame, snaps to the server position past a generous drift threshold
  (the Player keeps predicting locally with real collision), renders other
  players from snapshots (labelled capsules, lerped -- avatar appearance
  sync is a follow-up, the server doesn't replicate loadouts yet), and
  returns to the world list on disconnect.
- player.gd: exposes net_input (the input frame it applied) and
  apply_server_correction().
- network_client.gd: send_input() + get_own_server_state() for callers that
  do their own collision-aware prediction.
- scripts/mp_game_flow_client.gd + run_game_multiplayer_test.sh: two real
  clients each register -> join via the API -> game.tscn -> networked;
  A sees B and moves. PASS.

Verified end to end against an orchestration-enabled backend. Non-networked
smokes green (enter_world 9/9, world_list 5/5, player 15/15,
avatar_in_world 10/10, main_menu_full_flow 12/12).

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_015jtxAiu5dAW4WxCNdGkrkJ

scripts/game.gd

@@ -0,0 +1,141 @@
+extends Node3D
+## Root controller for scenes/game.tscn.
+##
+## Local single-player by default (walk around the test level). When
+## Session.active (set by world_list.gd after POST /api/worlds/{id}/join),
+## connects a NetworkClient to the world's dedicated server and runs
+## networked: the local Player keeps predicting with its own collision-aware
+## movement, its input is forwarded to the server each physics frame, the
+## server's authoritative position is a correction backstop, and other
+## players are rendered from snapshots.
+##
+## Appearance sync is a follow-up -- remote players show as labelled capsules,
+## not their own avatars (the server doesn't replicate loadouts yet).
+
+const REMOTE_LERP := 12.0
+## Snap the local player to the server position past this drift (metres).
+## Generous -- only catches real desync / teleport / a wall the client walked
+## through, not normal prediction noise.
+const CORRECTION_THRESHOLD := 1.5
+
+@onready var _player: Player = $Player
+
+var _net: NetworkClient = null
+var _networked := false
+var _remotes: Dictionary = {}   # peer_id -> Node3D
+var _status_label: Label = null
+
+
+func _ready() -> void:
+	if Session.active:
+		_setup_networked()
+
+
+func _setup_networked() -> void:
+	_show_status("Connecting to %s…" % Session.host)
+	_net = NetworkClient.new()
+	_net.name = "NetworkClient"
+	add_child(_net)
+	_net.server_disconnected.connect(_on_server_lost)
+	_net.connection_failed.connect(_on_server_lost)
+
+	var ok: bool = await _net.connect_to_server(Session.host, Session.port)
+	if not ok:
+		_on_server_lost()
+		return
+	_networked = true
+	_hide_status()
+	# Physics-process AFTER the player so net_input reflects this frame.
+	process_physics_priority = 10
+
+
+func _physics_process(_delta: float) -> void:
+	if not _networked or _net == null or not _net.is_connected_to_server():
+		return
+
+	# 1. Forward the local player's input to the server.
+	var inp: Dictionary = _player.net_input
+	_net.send_input(inp["move_x"], inp["move_z"], inp["jump"], inp["look_yaw"])
+
+	# 2. Server-authoritative correction backstop.
+	var own: Dictionary = _net.get_own_server_state()
+	if own.has("position"):
+		var server_pos: Vector3 = own["position"]
+		if _player.global_position.distance_to(server_pos) > CORRECTION_THRESHOLD:
+			_player.apply_server_correction(server_pos)
+
+	# 3. Remote players.
+	_sync_remotes(_net.get_remote_states(), _delta)
+
+
+func _sync_remotes(states: Dictionary, delta: float) -> void:
+	for pid in states:
+		var st: Dictionary = states[pid]
+		var node: Node3D = _remotes.get(pid)
+		if node == null:
+			node = _make_remote(pid)
+			_remotes[pid] = node
+			add_child(node)
+			node.global_position = st.get("position", Vector3.ZERO)
+		var target: Vector3 = st.get("position", node.global_position)
+		node.global_position = node.global_position.lerp(target, clampf(REMOTE_LERP * delta, 0.0, 1.0))
+		node.rotation.y = st.get("rotation_y", node.rotation.y)
+
+	for pid in _remotes.keys():
+		if not states.has(pid):
+			_remotes[pid].queue_free()
+			_remotes.erase(pid)
+
+
+func _make_remote(pid: int) -> Node3D:
+	var root := Node3D.new()
+	root.name = "Remote_%d" % pid
+
+	var body := MeshInstance3D.new()
+	var capsule := CapsuleMesh.new()
+	capsule.radius = 0.35
+	capsule.height = 1.7
+	body.mesh = capsule
+	body.position = Vector3(0, 0.85, 0)
+	var mat := StandardMaterial3D.new()
+	mat.albedo_color = Color.from_hsv(fmod(float(pid) * 0.61803, 1.0), 0.6, 0.9)
+	body.material_override = mat
+	root.add_child(body)
+
+	var tag := Label3D.new()
+	tag.text = "Player %d" % pid
+	tag.position = Vector3(0, 2.0, 0)
+	tag.billboard = BaseMaterial3D.BILLBOARD_ENABLED
+	tag.no_depth_test = true
+	tag.pixel_size = 0.004
+	root.add_child(tag)
+
+	return root
+
+
+func _on_server_lost() -> void:
+	_networked = false
+	_show_status("Disconnected from the server. Returning to worlds…")
+	await get_tree().create_timer(1.5).timeout
+	Session.clear()
+	get_tree().change_scene_to_file("res://scenes/world_list.tscn")
+
+
+# ─── tiny on-screen status ────────────────────────────────────────────────────
+
+func _show_status(text: String) -> void:
+	if _status_label == null:
+		var layer := CanvasLayer.new()
+		layer.name = "StatusLayer"
+		add_child(layer)
+		_status_label = Label.new()
+		_status_label.position = Vector2(16, 16)
+		_status_label.add_theme_font_size_override("font_size", 18)
+		layer.add_child(_status_label)
+	_status_label.text = text
+	_status_label.visible = true
+
+
+func _hide_status() -> void:
+	if _status_label:
+		_status_label.visible = false