[3.8] AioHTTPTestCase more async friendly (#4732)

[asvetlov]

Co-authored-by: Andrew Svetlov [email protected].
(cherry picked from commit 5357858)

Co-authored-by: Anas [email protected]

[codecov]

Codecov Report

Merging #5257 (2efdf95) into 3.8 (493221b) will not change coverage.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##              3.8    #5257   +/-   ##
=======================================
  Coverage   97.53%   97.53%           
=======================================
  Files          44       44           
  Lines        8844     8844           
  Branches     1424     1426    +2     
=======================================
  Hits         8626     8626           
  Misses        102      102           
  Partials      116      116           

Flag	Coverage Δ
unit	97.35% <84.61%> (-0.03%)	⬇️

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Impacted Files	Coverage Δ
aiohttp/test_utils.py	99.37% <100.00%> (ø)

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