docs: fix Lobby plan (_broadcast_player_left, cd commands) and spec

docs/plans/2026-04-13-lobby-rollen-design.md

@@ -58,7 +58,7 @@ signal game_started()
 
 ### Anpassung: `_on_peer_disconnected`
 
-Beide Dicts bereinigen und beide Signale emittieren:
+Server bereinigt lokal und broadcastet den Disconnect an alle anderen Clients:
 
 ```gdscript
 func _on_peer_disconnected(id: int) -> void:
@@ -66,9 +66,20 @@ func _on_peer_disconnected(id: int) -> void:
     players.erase(id)
     peer_disconnected.emit(id)
     player_left.emit(id)
+    _broadcast_player_left.rpc(id)  # andere Clients informieren
     print("[Server] Peer getrennt: %d" % id)
 ```
 
+### Neues RPC: `_broadcast_player_left` (Server → alle anderen Clients)
+
+```gdscript
+# call_remote: Server hat bereits lokal gelöscht; nur Clients führen aus
+@rpc("authority", "call_remote", "reliable")
+func _broadcast_player_left(peer_id: int) -> void:
+    players.erase(peer_id)
+    player_left.emit(peer_id)
+```
+
 ### Neues RPC: `register` (Client → Server)
 
 ```gdscript

docs/plans/2026-04-13-lobby-rollen-plan.md

@@ -53,6 +53,7 @@ func _on_peer_disconnected(id: int) -> void:
 	players.erase(id)
 	peer_disconnected.emit(id)
 	player_left.emit(id)
+	_broadcast_player_left.rpc(id)
 	print("[Server] Peer getrennt: %d" % id)
 ```
 
@@ -130,6 +131,13 @@ func request_start_game() -> void:
 @rpc("authority", "call_local", "reliable")
 func start_game() -> void:
 	game_started.emit()
+
+
+# call_remote: Server hat lokal bereits gelöscht; nur Clients führen aus
+@rpc("authority", "call_remote", "reliable")
+func _broadcast_player_left(peer_id: int) -> void:
+	players.erase(peer_id)
+	player_left.emit(peer_id)
 ```
 
 - [ ] **Step 2: Einrückung prüfen (Tabs, nicht Spaces)**
@@ -366,7 +374,7 @@ git commit -m "net: add lobby scene instance to main.tscn"
 - [ ] **Step 1: Server headless starten**
 
 ```bash
-# aus ruf-der-pilze/
+cd /home/mpuchstein/Dev/Godot/DnD_Anna_OneShot/ruf-der-pilze
 godot --headless -- --server
 ```
 
@@ -396,8 +404,7 @@ Server-Terminal:
 
 Zweiten Godot-Prozess starten (z.B. über Terminal):
 ```bash
-# aus ruf-der-pilze/
-godot
+cd /home/mpuchstein/Dev/Godot/DnD_Anna_OneShot/ruf-der-pilze && godot
 ```
 
 Name "Marie", Rolle "DM", "Beitreten".