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To start out sharing what I found in the Django code:
Here inside BaseHandler._get_response_async():
https://github.com/django/django/blob/3460ea49e839fd6bb924c48eaa1cd3d6dc888035/django/core/handlers/base.py#L226-L232
try:
 response = await wrapped_callback(request, *callback_args,
 **callback_kwargs)
except Exception as e:
 response = await sync_to_async( # This line hangs.
 self.process_exception_by_middleware,
 thread_sensitive=True,
 )(e, request)
you can see an exception being handled, which is then passed to process_exception_by_middleware(). Process_exception_by_middleware() can wind up re-raising that same exception, which causes __context__ to be set circularly inside the except block:
https://github.com/django/django/blob/3460ea49e839fd6bb924c48eaa1cd3d6dc888035/django/core/handlers/base.py#L323-L332
If you boil this down, you get the following as a simple reproducer. This doesn't hang, but you can tell the difference by comparing exc2 to exc2.__context as indicated below:
import asyncio
async def process_exc(exc):
 raise exc
async def run():
 try:
 raise RuntimeError
 except Exception as exc:
 task = asyncio.create_task(process_exc(exc))
 try:
 await task
 except BaseException as exc2:
 # Prints True in 3.9.0b1 and False in 3.9.0a6.
 print(exc2 is exc2.__context__)
loop = asyncio.new_event_loop()
try:
 loop.run_until_complete(run())
finally:
 loop.close()
 
The cause is probably the following PR, which enabled exception chaining for gen.throw() in the yield from case:
https://github.com/python/cpython/pull/19858
So the answer might be to do some cycle detection when chaining the exception, which apparently _PyErr_ChainExceptions() doesn't do.