fix(docs): add lifespan for fastapi

Author: m-xim

docs/engines/token-engine.md

@@ -123,7 +123,7 @@ async def set_webhooks(app):
     await engine.add_bot("654321:UVWXYZ")
 ```
 
-`engine.register(app)` wires local framework callbacks. `engine.add_bot()` resolves the bot and calls Telegram.
+`engine.register(app)` registers the local route (with aiohttp, also wires lifecycle callbacks). For FastAPI, wrap startup in `engine.lifespan(app)` — see [FastAPI adapter](../web/fastapi.md). `engine.add_bot()` resolves the bot and calls Telegram.
 
 ### shutdown_timeout
 

docs/index.yaml

@@ -141,8 +141,9 @@ blocks:
 
           @asynccontextmanager
           async def lifespan(app: FastAPI):
-              await engine.set_webhook()
-              yield
+              async with engine.lifespan(app):
+                  await engine.set_webhook()
+                  yield
 
 
           app = FastAPI(lifespan=lifespan)

docs/web/custom.md

@@ -4,7 +4,7 @@ Create a custom adapter when your web framework is not FastAPI or aiohttp. The a
 
 `FastAPIAdapter` and `AiohttpAdapter` are shipped reference implementations — useful to read, not mandatory templates. Study their source when you need working lifecycle wiring or multipart reply handling:
 
-* `aiogram_webhook.web.fastapi` — router lifespan, Starlette payload bridge
+* `aiogram_webhook.web.fastapi` — `engine.lifespan(app)` context manager pattern, Starlette payload bridge
 * `aiogram_webhook.web.aiohttp` — `web.Application` routes and startup/shutdown hooks
 
 See also [Extending overview](../custom-integrations.md) for how adapters fit next to engines and security.