Let me preface this by declaring that I am very new to Python async so it is very possible that I am missing something seemingly obvious. That being said, I've been looking at various resources to try to understand the internals of asyncio and it hasn't led to any insights on this problem thus far.
-----------------

This all sounds quite similar to an experience I am dealing with. I'm working with pub sub within aioredis which internally uses a StreamReader with a function equivalent to readexactly. This all started from debugging "Task was destroyed but it is pending!" to which attempted fixes led to multiple "RuntimeError: aclose(): asynchronous generator is already running" errors.

I did the same thing, adding try excepts everywhere in my code to understand what was happening and this led me to identifying that a regular async function would raise GeneratorExit during await. However, even if I suppress this, the caller awaiting on this function would also raise a GeneratorExit. Suppressing this exception at the top level leads to an unsuspecting (to me) error "coroutine ignored GeneratorExit".

I understand that GeneratorExit is raised in unfinished generators when garbage collected to handle cleanup. And I understand that async functions are essentially a generator in the sense that they yield when they await. So, if the entire coroutine were garbage collected this might trigger GeneratorExit in each nested coroutine. However, from all of my logging I am sure that prior to the GeneratorExit, nothing returns  upwards so there should still be valid references to every object.

I'll include some errors below, in case they may be of relevance:

=== Exception in await of inner async function ===
Traceback (most recent call last):
  File ".../site-packages/uvicorn/protocols/http/httptools_impl.py", line 165, in data_received
    self.parser.feed_data(data)
  File "httptools/parser/parser.pyx", line 196, in httptools.parser.parser.HttpParser.feed_data
httptools.parser.errors.HttpParserUpgrade: 858

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File ".../my_code.py", line 199, in wait_for_update
    return await self.waiter.wait_for_value()
GeneratorExit

=== Exception when suppressing GeneratorExit on the top level ===
Exception ignored in: <coroutine object parent_async_function at 0x0b...>
Traceback (most recent call last):
  File ".../site-packages/websockets/protocol.py", line 229, in __init__
    self.reader = asyncio.StreamReader(limit=read_limit // 2, loop=loop)
RuntimeError: coroutine ignored GeneratorExit