Serve API and website behind Caddy path prefixes

Caddy forwards /wizard/api/* and /wizard/website/* with the prefix
stripped, so the server received /ws instead of /api/ws and the website
connected to /api/ws on the domain root.

- Server routes are now /ws and /health (was /api/ws, /api/health)
- Website derives the websocket URL from its own location (../api/ws),
  giving /wizard/api/ws in production and /api/ws in development
- Vite dev proxy strips /api like the production proxy
- nginx back to the plain SPA config since Caddy strips the prefix
- /internal/ai rejects requests that came through the reverse proxy,
  in addition to the shared secret
- Docs updated for the prefixed deployment

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

wizard_server/tests/test_server.py

@@ -32,7 +32,7 @@ def is_state(message):
 
 
 def connect(client, token=None):
-    ws = client.sockets.enter_context(client.websocket_connect("/api/ws"))
+    ws = client.sockets.enter_context(client.websocket_connect("/ws"))
     ws.send_json({"type": "hello", "token": token})
     welcome = receive_until(ws, lambda m: m["type"] == "welcome")
     receive_until(ws, is_state)
@@ -40,13 +40,13 @@ def connect(client, token=None):
 
 
 def test_health(client):
-    response = client.get("/api/health")
+    response = client.get("/health")
     assert response.status_code == 200
     assert response.json()["status"] == "ok"
 
 
 def test_requires_hello(client):
-    with client.websocket_connect("/api/ws") as ws:
+    with client.websocket_connect("/ws") as ws:
         ws.send_json({"type": "create_lobby", "name": "Ann"})
         assert ws.receive_json()["type"] == "error"
 
@@ -118,7 +118,7 @@ def test_reconnect_with_token(client):
     code = receive_until(ws, is_state)["lobby"]["code"]
     ws.close()
 
-    ws2 = client.sockets.enter_context(client.websocket_connect("/api/ws"))
+    ws2 = client.sockets.enter_context(client.websocket_connect("/ws"))
     ws2.send_json({"type": "hello", "token": welcome["token"]})
     again = receive_until(ws2, lambda m: m["type"] == "welcome")
     assert again["player_id"] == welcome["player_id"]
@@ -153,6 +153,15 @@ def test_ai_endpoint_requires_secret(client):
             ws.receive_json()
 
 
+def test_ai_endpoint_rejects_proxied_requests(client):
+    from starlette.websockets import WebSocketDisconnect
+
+    headers = {"Authorization": f"Bearer {SECRET}", "X-Forwarded-For": "203.0.113.7"}
+    with pytest.raises(WebSocketDisconnect):
+        with client.websocket_connect("/internal/ai", headers=headers) as ws:
+            ws.receive_json()
+
+
 def test_ai_service_decides(client):
     """A fake AI service answers decide requests with the first legal action."""
     requests = []