Fix AsyncResolver to match ThreadedResolver behavior (#8270)

[bdraco]

Co-authored-by: Sviatoslav Sydorenko (Святослав Сидоренко) sviat@redhat.com
(cherry picked from commit 012f986)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.51%. Comparing base (6643115) to head (65d051d).
Report is 1 commits behind head on 3.10.

Additional details and impacted files

@@            Coverage Diff             @@
##             3.10    #8295      +/-   ##
==========================================
- Coverage   97.52%   97.51%   -0.01%     
==========================================
  Files         108      108              
  Lines       33196    33247      +51     
  Branches     3956     3960       +4     
==========================================
+ Hits        32373    32422      +49     
- Misses        620      622       +2     
  Partials      203      203              

Flag	Coverage Δ
CI-GHA	97.42% <100.00%> (-0.01%)	⬇️
OS-Linux	97.10% <99.18%> (-0.01%)	⬇️
OS-Windows	94.74% <67.47%> (+<0.01%)	⬆️
OS-macOS	96.82% <99.18%> (-0.01%)	⬇️
Py-3.10.11	94.55% <67.47%> (+<0.01%)	⬆️
Py-3.10.14	96.89% <99.18%> (-0.01%)	⬇️
Py-3.11.8	97.08% <100.00%> (-0.01%)	⬇️
Py-3.12.2	97.19% <100.00%> (-0.01%)	⬇️
Py-3.8.10	94.48% <55.28%> (-0.05%)	⬇️
Py-3.8.18	96.73% <78.04%> (-0.10%)	⬇️
Py-3.9.13	94.54% <67.47%> (+<0.01%)	⬆️
Py-3.9.19	96.87% <99.18%> (+0.01%)	⬆️
Py-pypy7.3.15	96.39% <99.18%> (-0.01%)	⬇️
VM-macos	96.82% <99.18%> (-0.01%)	⬇️
VM-ubuntu	97.10% <99.18%> (-0.01%)	⬇️
VM-windows	94.74% <67.47%> (+<0.01%)	⬆️

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