fix(mcp-docugen): mount FastMCP a root + lifespan session_manager.run()

- streamable_http_app() espone /mcp internamente; mount a root evita doppio prefisso.
- mcp.session_manager.run() integrato nel lifespan FastAPI: l'app mounted non
  riceve automaticamente il proprio lifespan -> la task group streamable-http
  non veniva inizializzata e le richieste MCP fallivano con RuntimeError.

Smoke test end-to-end via gateway Caddy (porta 8090):
- MCP initialize handshake OK
- tools/list espone 6 tool corretti
- template_create + template_list: round-trip con persistenza su volume
- document_generate propaga LLMAuthError come MCP isError:true
- Registrato in claude mcp list: ✓ Connected

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

services/mcp-docugen/src/mcp_docugen/main.py

@@ -49,24 +49,27 @@ async def build_app(settings: Settings | None = None) -> FastAPI:
     )
 
     mcp = build_mcp_server(template_store, renderer)
+    mcp_asgi = mcp.streamable_http_app()
 
     @asynccontextmanager
     async def lifespan(app: FastAPI):
-        cleanup_task = asyncio.create_task(
-            _periodic_cleanup(generation_store, interval_seconds=24 * 3600)
-        )
-        try:
-            yield
-        finally:
-            cleanup_task.cancel()
+        async with mcp.session_manager.run():
+            cleanup_task = asyncio.create_task(
+                _periodic_cleanup(generation_store, interval_seconds=24 * 3600)
+            )
             try:
-                await cleanup_task
-            except asyncio.CancelledError:
-                pass
+                yield
+            finally:
+                cleanup_task.cancel()
+                try:
+                    await cleanup_task
+                except asyncio.CancelledError:
+                    pass
 
     app = build_http_app(template_store, generation_store)
     app.router.lifespan_context = lifespan
-    app.mount("/mcp", mcp.streamable_http_app())
+    # streamable_http_app() espone /mcp internamente; monto a root.
+    app.mount("/", mcp_asgi)
 
     app.add_middleware(
         ApiKeyAuthMiddleware,