fix: support mounting StaticFiles to APIRouter, raise error for other apps

- Override APIRouter.mount() to only allow StaticFiles; raise FastAPIError
  for any other ASGI app with a clear error message
- Add APIRouter._mount() as internal method used by include_router()
  and FastAPI.mount() to bypass the StaticFiles-only restriction
- Override FastAPI.mount() to call self.router._mount() directly
- Propagate StaticFiles mounts in include_router() via _mount()
- Rename test file to test_apirouter_mount.py

Fixes #10180

fastapi/routing.py

@@ -996,18 +996,12 @@ class APIRouter(routing.Router):
 
     def mount(self, path: str, app: ASGIApp, name: str | None = None) -> None:
         """
-        Mount a `StaticFiles` instance at the given path.
-
-        Raises `FastAPIError` if `app` is not an instance of `StaticFiles`,
-        since mounting arbitrary ASGI sub-applications under an `APIRouter`
-        is not supported. Sub-applications should be mounted directly on
-        the root `FastAPI` instance instead.
+        Mount a StaticFiles instance.
+        Will raise a FastAPIError exception if app is not an instance of StaticFiles.
         """
         if not isinstance(app, StaticFiles):
             raise FastAPIError(
-                "APIRouter does not support mounting ASGI applications other than "
-                "StaticFiles. Mount sub-applications directly on the root FastAPI "
-                "instance instead."
+                "APIRouter does not support mounting ASGI applications other than StaticFiles."
             )
         self._mount(path=path, app=app, name=name)
 

tests/test_router_mount.py → tests/test_apirouter_mount.py

@@ -76,6 +76,6 @@ def test_mount_non_staticfiles_app_raises_error() -> None:
 
     with pytest.raises(
         FastAPIError,
-        match="APIRouter does not support mounting ASGI applications other than StaticFiles",
+        match="APIRouter does not support mounting ASGI applications other than StaticFiles.",
     ):
         router.mount("/sub", sub_app)