websocket: Async version of WebSocketHandler.close is needed

NOTE: this is different from https://github.com/tornadoweb/tornado/issues/2763. possibly related to https://github.com/tornadoweb/tornado/issues/2448, but also distinct.

After starting a websocket server, I am getting

ERROR:asyncio:Task was destroyed but it is pending!
task: <Task pending name='Task-5' coro=<RequestHandler._execute() running at /usr/local/lib/python3.8/site-packages/tornado/web.py:1703> wait_for=<Future pending cb=[<TaskWakeupMethWrapper object at 0x10acb2970>()]> cb=[_HandlerDelegate.execute.<locals>.<lambda>() at /usr/local/lib/python3.8/site-packages/tornado/web.py:2333]>

even after appropriately closing all connections. this is different from https://github.com/tornadoweb/tornado/issues/2763, where the unresolved task was WebSocketProtocol13._receive_frame_loop, and not all connections were closed.

to reproduce this easily, run the following tiny python3 program:

import asyncio
from abc import ABC
import tornado.websocket
import tornado.httpserver
import tornado.ioloop
import tornado.web

handlers = []
class Handler(tornado.websocket.WebSocketHandler, ABC):
    def open(self):  # making this async and awaiting write_message doesn't silence the tornado warnings.
        handlers.append(self)
    def on_message(self, message):
        pass
    def on_close(self):
        pass
    def check_origin(self, origin):
        return True
application = tornado.web.Application([
    (r'/', Handler),
])
http_server = tornado.httpserver.HTTPServer(application)
loop = tornado.ioloop.IOLoop.current()
async def my_function():  # closes the connections, stops the server, stops the loop after 20s.
    await asyncio.sleep(20.0)
    for handler in handlers:
        handler.close()
    http_server.stop()
    loop.stop()
http_server.listen(8080)
loop.add_callback(my_function)
loop.start()
loop.close()

in a separate Node.js console (for example), run:

const WebSocket = require('ws');
new WebSocket('ws://localhost:8080')

the culprit appears to be the future fut here, which is never awaited:
https://github.com/tornadoweb/tornado/blob/79b9c4fcbb3728f1325c4f6120bec45dd5df9fd8/tornado/web.py#L2323-L2326
tornado version: tornado-6.0.4. Python version: 3.8.5.

i am unable to further diagnose the issue, or fix it. thanks for your attention and time.

Start with tornado/web.py around the cited lines 2323-2326 and inspect how the reproduced WebSocketHandler is closed. Run the provided Python server with a Node.js WebSocket client, then verify the connection shutdown leaves no pending-task warning after the server and loop stop. Done means an asynchronous close path is available and the reproduction completes without the reported warning.