Fix graceful shutdown with keep-alive connections

[Dreamsorcerer]

Included into #7718

[codecov]

Codecov Report

Merging #7699 (f838406) into master (3d60762) will decrease coverage by 0.03%.
Report is 6 commits behind head on master.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master    #7699      +/-   ##
==========================================
- Coverage   97.36%   97.34%   -0.03%     
==========================================
  Files         106      106              
  Lines       31630    31690      +60     
  Branches     3619     3629      +10     
==========================================
+ Hits        30797    30849      +52     
- Misses        630      639       +9     
+ Partials      203      202       -1     

Flag	Coverage Δ
CI-GHA	97.26% <100.00%> (-0.03%)	⬇️
OS-Linux	96.93% <100.00%> (-0.02%)	⬇️
OS-Windows	95.41% <100.00%> (-0.02%)	⬇️
OS-macOS	96.60% <100.00%> (-0.02%)	⬇️
Py-3.10.11	95.34% <100.00%> (-0.02%)	⬇️
Py-3.10.13	96.79% <100.00%> (-0.02%)	⬇️
Py-3.11.5	96.47% <96.15%> (-0.08%)	⬇️
Py-3.8.10	95.31% <100.00%> (-0.02%)	⬇️
Py-3.8.18	96.73% <100.00%> (-0.02%)	⬇️
Py-3.9.13	95.30% <100.00%> (-0.02%)	⬇️
Py-3.9.18	96.75% <100.00%> (-0.02%)	⬇️
Py-pypy7.3.11	96.25% <100.00%> (-0.03%)	⬇️
VM-macos	96.60% <100.00%> (-0.02%)	⬇️
VM-ubuntu	96.93% <100.00%> (-0.02%)	⬇️
VM-windows	95.41% <100.00%> (-0.02%)	⬇️

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Files	Coverage Δ
aiohttp/web_runner.py	97.85% <100.00%> (+0.01%)	⬆️
aiohttp/web_server.py	95.34% <100.00%> (+0.34%)	⬆️
tests/test_run_app.py	98.33% <100.00%> (+0.07%)	⬆️

... and 6 files with indirect coverage changes

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