WebSocketRoute does not work with functools.partial

[connection-reset]

Checklist

• The bug is reproducible against the latest release and/or master.
• There are no similar issues or pull requests to fix it yet.

Describe the bug

Accessing a WebSocketRoute with async function wrapped in functools.partial raises TypeError.

To reproduce

import functools
from starlette.applications import Starlette
from starlette.routing import WebSocketRoute

async def handle_ws(ws):
    pass

app = Starlette(debug=True, routes=[
    WebSocketRoute("/", functools.partial(handle_ws)),
])

Install uvicorn[standard], run with uvicorn bug:app.
Access ws://localhost:8000 with e.g. wscat.

Expected behavior

WebSocketRoute should work with functools.partial just like Route.

Actual behavior

The route fails because it is treated as an ASGI application (ref.

starlette/starlette/routing.py

Lines 279 to 284 in f53faba

	if inspect.isfunction(endpoint) or inspect.ismethod(endpoint):
	# Endpoint is function or method. Treat it as `func(websocket)`.
	self.app = websocket_session(endpoint)
	else:
	# Endpoint is a class. Treat it as ASGI.
	self.app = endpoint

).

Debugging material

Traceback (most recent call last):
  File "/tmp/bug/venv/lib/python3.9/site-packages/uvicorn/protocols/websockets/websockets_impl.py", line 199, in run_asgi
    result = await self.app(self.scope, self.asgi_receive, self.asgi_send)
  File "/tmp/bug/venv/lib/python3.9/site-packages/uvicorn/middleware/proxy_headers.py", line 75, in __call__
    return await self.app(scope, receive, send)
  File "/tmp/bug/venv/lib/python3.9/site-packages/starlette/applications.py", line 112, in __call__
    await self.middleware_stack(scope, receive, send)
  File "/tmp/bug/venv/lib/python3.9/site-packages/starlette/middleware/errors.py", line 146, in __call__
    await self.app(scope, receive, send)
  File "/tmp/bug/venv/lib/python3.9/site-packages/starlette/exceptions.py", line 58, in __call__
    await self.app(scope, receive, send)
  File "/tmp/bug/venv/lib/python3.9/site-packages/starlette/routing.py", line 656, in __call__
    await route.handle(scope, receive, send)
  File "/tmp/bug/venv/lib/python3.9/site-packages/starlette/routing.py", line 315, in handle
    await self.app(scope, receive, send)
TypeError: handle_ws() takes 1 positional argument but 3 were given

Environment

• OS: Arch Linux
• Python version: 3.9.9
• Starlette version: 0.17.1

Additional context

Support for functools.partial for Route was introduced in #984.
Those changes to Route.__init__ fix this bug too but just copying them feels unsustainable.

[Kludex]

Sounds reasonable. PR is welcome.