Fix flaky websocket test

[Dreamsorcerer]

Hopefully fixes the flakiness, by allowing a little extra time. Also improved the test by actually testing the client behaviour, and removing some calls which did nothing.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (9a7cfe7) 97.40% compared to head (4f7b304) 97.40%.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #7902   +/-   ##
=======================================
  Coverage   97.40%   97.40%           
=======================================
  Files         107      107           
  Lines       32246    32247    +1     
  Branches     3750     3750           
=======================================
+ Hits        31410    31411    +1     
  Misses        632      632           
  Partials      204      204           

Flag	Coverage Δ
CI-GHA	97.32% <100.00%> (+<0.01%)	⬆️
OS-Linux	96.99% <100.00%> (+<0.01%)	⬆️
OS-Windows	95.48% <100.00%> (+<0.01%)	⬆️
OS-macOS	96.80% <100.00%> (-0.01%)	⬇️
Py-3.10.11	95.41% <100.00%> (+<0.01%)	⬆️
Py-3.10.13	96.79% <100.00%> (+<0.01%)	⬆️
Py-3.11.5	?
Py-3.11.6	96.50% <100.00%> (+<0.01%)	⬆️
Py-3.12.0	96.60% <100.00%> (+0.02%)	⬆️
Py-3.8.10	95.37% <100.00%> (+<0.01%)	⬆️
Py-3.8.18	96.72% <100.00%> (+<0.01%)	⬆️
Py-3.9.13	95.37% <100.00%> (+<0.01%)	⬆️
Py-3.9.18	96.76% <100.00%> (+<0.01%)	⬆️
Py-pypy7.3.13	96.22% <100.00%> (+<0.01%)	⬆️
VM-macos	96.80% <100.00%> (-0.01%)	⬇️
VM-ubuntu	96.99% <100.00%> (+<0.01%)	⬆️
VM-windows	95.48% <100.00%> (+<0.01%)	⬆️

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[patchback]

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

❌ Failed to cleanly apply 28d0b06 on top of patchback/backports/3.9/28d0b06c267335555f46569d0fd8803b74b1a5a4/pr-7902

Backporting merged PR #7902 into master

1. Ensure you have a local repo clone of your fork. Unless you cloned it
   from the upstream, this would be your origin remote.
2. 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

3. 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/3.9/28d0b06c267335555f46569d0fd8803b74b1a5a4/pr-7902 upstream/3.9

4. Now, cherry-pick PR Fix flaky websocket test #7902 contents into that branch:

   $ git cherry-pick -x 28d0b06c267335555f46569d0fd8803b74b1a5a4

   If it'll yell at you with something like fatal: Commit 28d0b06c267335555f46569d0fd8803b74b1a5a4 is a merge but no -m option was given., add -m 1 as follows instead:

   $ git cherry-pick -m1 -x 28d0b06c267335555f46569d0fd8803b74b1a5a4

5. At this point, you'll probably encounter some merge conflicts. You must
   resolve them in to preserve the patch from PR Fix flaky websocket test #7902 as close to the
   original as possible.
6. Push this branch to your fork on GitHub:

   $ git push origin patchback/backports/3.9/28d0b06c267335555f46569d0fd8803b74b1a5a4/pr-7902

7. 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!

🤖 @patchback
I'm built with octomachinery and
my source is open — /~https://github.com/sanitizers/patchback-github-app.

[patchback]

Backport to 3.10: 💔 cherry-picking failed — conflicts found

❌ Failed to cleanly apply 28d0b06 on top of patchback/backports/3.10/28d0b06c267335555f46569d0fd8803b74b1a5a4/pr-7902

Backporting merged PR #7902 into master

1. Ensure you have a local repo clone of your fork. Unless you cloned it
   from the upstream, this would be your origin remote.
2. 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

3. 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/3.10/28d0b06c267335555f46569d0fd8803b74b1a5a4/pr-7902 upstream/3.10

4. Now, cherry-pick PR Fix flaky websocket test #7902 contents into that branch:

   $ git cherry-pick -x 28d0b06c267335555f46569d0fd8803b74b1a5a4

   If it'll yell at you with something like fatal: Commit 28d0b06c267335555f46569d0fd8803b74b1a5a4 is a merge but no -m option was given., add -m 1 as follows instead:

   $ git cherry-pick -m1 -x 28d0b06c267335555f46569d0fd8803b74b1a5a4

5. At this point, you'll probably encounter some merge conflicts. You must
   resolve them in to preserve the patch from PR Fix flaky websocket test #7902 as close to the
   original as possible.
6. Push this branch to your fork on GitHub:

   $ git push origin patchback/backports/3.10/28d0b06c267335555f46569d0fd8803b74b1a5a4/pr-7902

7. 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!

🤖 @patchback
I'm built with octomachinery and
my source is open — /~https://github.com/sanitizers/patchback-github-app.