[PR #10946/3c88f811 backport][3.12] Ensure AsyncResolver.close() can be called multiple times

[patchback]

This is a backport of PR #10946 as merged into master (3c88f81).

regressed in #10847 but never in a stable release so I linked the changelog message instead of adding a bugfix.

[codspeed-hq]

CodSpeed Performance Report

Merging #10947 will not alter performance

_{Comparing patchback/backports/3.12/3c88f811390cebf524281bebfdbd807a57ab855e/pr-10946 (9817c0e) with 3.12 (9bd43ed)}

Summary

✅ 59 untouched benchmarks

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.16%. Comparing base (9bd43ed) to head (9817c0e).
Report is 1 commits behind head on 3.12.

✅ All tests successful. No failed tests found.

Additional details and impacted files

@@           Coverage Diff           @@
##             3.12   #10947   +/-   ##
=======================================
  Coverage   98.16%   98.16%           
=======================================
  Files         130      130           
  Lines       39655    39675   +20     
  Branches     2241     2242    +1     
=======================================
+ Hits        38928    38948   +20     
  Misses        555      555           
  Partials      172      172           

Flag	Coverage Δ
CI-GHA	98.05% <100.00%> (+<0.01%)	⬆️
OS-Linux	97.77% <100.00%> (+<0.01%)	⬆️
OS-Windows	95.26% <100.00%> (+<0.01%)	⬆️
OS-macOS	96.94% <100.00%> (+<0.01%)	⬆️
Py-3.10.11	96.83% <100.00%> (+<0.01%)	⬆️
Py-3.10.17	97.37% <100.00%> (-0.01%)	⬇️
Py-3.11.12	97.47% <100.00%> (-0.01%)	⬇️
Py-3.11.9	96.94% <100.00%> (+<0.01%)	⬆️
Py-3.12.10	97.83% <100.00%> (+<0.01%)	⬆️
Py-3.13.3	97.83% <100.00%> (+<0.01%)	⬆️
Py-3.9.13	96.72% <100.00%> (+<0.01%)	⬆️
Py-3.9.22	97.25% <100.00%> (+<0.01%)	⬆️
Py-pypy7.3.16	82.70% <100.00%> (-4.62%)	⬇️
VM-macos	96.94% <100.00%> (+<0.01%)	⬆️
VM-ubuntu	97.77% <100.00%> (+<0.01%)	⬆️
VM-windows	95.26% <100.00%> (+<0.01%)	⬆️

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