Restore async concurrency safety to websocket compressor #7865

Backport to 3.9: 💔 cherry-picking failed — conflicts found

❌ Failed to cleanly apply 86a2396 on top of patchback/backports/3.9/86a23961531103ccc34853f67321c7d0f63797f5/pr-7865

Ensure you have a local repo clone of your fork. Unless you cloned it
from the upstream, this would be your origin remote.
Make sure you have an upstream repo added as a remote too. In these
instructions you'll refer to it by the name upstream. If you don't
have it, here's how you can add it:
```
$ git remote add upstream https://github.com/aio-libs/aiohttp.git
```

Ensure you have the latest copy of upstream and prepare a branch
that will hold the backported code:

$ git fetch upstream
$ git checkout -b patchback/backports/3.9/86a23961531103ccc34853f67321c7d0f63797f5/pr-7865 upstream/3.9

Now, cherry-pick PR #7865 contents into that branch:
```
$ git cherry-pick -x 86a23961531103ccc34853f67321c7d0f63797f5
```
If it'll yell at you with something like fatal: Commit 86a23961531103ccc34853f67321c7d0f63797f5 is a merge but no -m option was given., add -m 1 as follows instead:
```
$ git cherry-pick -m1 -x 86a23961531103ccc34853f67321c7d0f63797f5
```
At this point, you'll probably encounter some merge conflicts. You must
resolve them in to preserve the patch from PR #7865 as close to the
original as possible.

Push this branch to your fork on GitHub:

$ git push origin patchback/backports/3.9/86a23961531103ccc34853f67321c7d0f63797f5/pr-7865

Create a PR, ensure that the CI is green. If it's not — update it so that
the tests and any other checks pass. This is it!
Now relax and wait for the maintainers to process your pull request
when they have some cycles to do reviews. Don't worry — they'll tell you if
any improvements are necessary when the time comes!