Context race condition with patch_stdout, ProgressBar and in_terminal

I am trying to print_formatted_text asynchronously while ProgressBar is running. I tried this:

import asyncio as aio

from prompt_toolkit.application import in_terminal
from prompt_toolkit import print_formatted_text
from prompt_toolkit.shortcuts import ProgressBar
from prompt_toolkit.patch_stdout import patch_stdout


async def log():
    await aio.sleep(1)
    count = 1
    while True:
        print_formatted_text(f'log{count}')
        count += 1
        await aio.sleep(.1)


async def progress():
    with ProgressBar() as pb:
        for _ in pb(range(100)):
            await aio.sleep(.1)
    loop.create_task(progress())


if __name__ == '__main__':
    with patch_stdout():
        loop = aio.get_event_loop()
        loop.create_task(log())
        loop.create_task(progress())
        loop.run_forever()

But print_formatted_text messed up the ProgressBar

log1.0% [==========>                                  ]   9/100 eta [00:09]
log2               ==>                                   11
log3                 ==>                                  2              8
log4                   ==>                                4
log5                     =>                               5
...

After some research of old issues and docs i tried to change print_formatted_text(f'log{count}') to

async with in_terminal():
    print_formatted_text(f'log{count}')

Everything prints as expected but sometimes throws an error:

Unhandled exception in event loop:
  File "C:\Python391\lib\asyncio\events.py", line 80, in _run
    self._context.run(self._callback, *self._args)
  File "D:\_Projects\python\bot\py\lib\site-packages\prompt_toolkit\eventloop\utils.py", line 77, in schedule
    func()
  File "D:\_Projects\python\bot\py\lib\site-packages\prompt_toolkit\application\application.py", line 476, in redraw
    self._redraw()
  File "D:\_Projects\python\bot\py\lib\site-packages\prompt_toolkit\application\application.py", line 543, in _redraw
    self.context.run(run_in_context)

Exception cannot enter context: <Context object at 0x00000233BE38AC80> is already entered

I tried to fix this by changing:
https://github.com/prompt-toolkit/python-prompt-toolkit/blob/c8fb6e2e6eae34fb57ac225a09565ba071f59fe5/prompt_toolkit/application/application.py#L542-L543
To:

if self.context is not None:
    call_soon_threadsafe(
        lambda: self.context.run(run_in_context),
        max_postpone_time = self.max_render_postpone_time,
        loop=self.loop,
    )

And it worked but not sure if this is correct way

Reproducable example

import asyncio as aio

from prompt_toolkit.application import in_terminal
from prompt_toolkit import print_formatted_text
from prompt_toolkit.shortcuts import ProgressBar
from prompt_toolkit.patch_stdout import patch_stdout


async def log():
    await aio.sleep(1)
    count = 1
    while True:
        async with in_terminal():
            print_formatted_text(f'log{count}')
        count += 1
        await aio.sleep(.2)


async def progress():
    with ProgressBar() as pb:
        for _ in pb(range(100)):
            await aio.sleep(.1)
    loop.create_task(progress())


if __name__ == '__main__':
    with patch_stdout():
        loop = aio.get_event_loop()
        loop.create_task(log())
        loop.create_task(progress())
        loop.run_forever()

My environment:

• windows 10
• python 3.9.1
• prompt-toolkit 3.0.14

Start with the reproducible asyncio example and inspect prompt_toolkit/application/application.py around lines 542-543, where the context is entered during redraw. Reproduce the interaction between patch_stdout, ProgressBar, and in_terminal, then verify that redraws no longer raise an already-entered-context error and that progress output remains intact.