WebSocket waits for next async task to finish before sending a message

[kapicic]

Description

When sending multiple consecutive messages via a WebSocket, all the messages are pending until the longest async task finishes and sends all the messages in a batch.

Steps to reproduce

# server.py
from starlette.websockets import WebSocket


async def app(scope, receive, send):
    websocket = WebSocket(scope=scope, receive=receive, send=send)
    await websocket.accept()
    await websocket.send_text('Hello world!')
    status = await some_very_long_function()
    await websocket.send_text(status)
    await websocket.send_text('Hello world again!')
    await websocket.close()

# lets say this runs for 2s
async def some_very_long_function():
    # important: must NOT be an asyncio call
    for i in range(300000000):
        _ = i + i

    return "done"

# client.py
import asyncio
import websockets

async def receive():
    async with websockets.connect('ws://localhost:8000') as websocket:
        try:
            while True:
                message = await websocket.recv()
                print(message)
        except websockets.exceptions.ConnectionClosed:
            print("Connection closed")

asyncio.get_event_loop().run_until_complete(receive())

1. uvicorn server:app
2. python -m client

Expected behaviour

'Hello world!'
2s pause
'done'
'Hello world again!'

Actual behaviour

2s pause
'Hello world!'
'done'
'Hello world again!'

Using asyncio

If we replace the blocking logic with await asyncio.sleep(2) we get expected behaviour.
Additionally, adding await asyncio.sleep(1) before the await some_very_long_function() results in expected behaviour:

# server.py
async def app(scope, receive, send):
    websocket = WebSocket(scope=scope, receive=receive, send=send)
    await websocket.accept()
    await websocket.send_text('Hello world!')
    await asyncio.sleep(1)
    status = await some_very_long_function()
    await websocket.send_text(status)
    await websocket.send_text('Hello world again!')
    await websocket.close()

Results in:

'Hello world!'
1s pause
2s pause
'done'
'Hello world again!'

[Kludex]

I cannot reproduce your experiment. I have the "expected" behavior here.