Remove unused async_run

[oyvindeide]

Approach
🧹

(Screenshot of new behavior in GUI if applicable)

• PR title captures the intent of the changes, and is fitting for release notes.
• Added appropriate release note label
• Commit history is consistent and clean, in line with the contribution guidelines.
• Make sure unit tests pass locally after every commit (git rebase -i main --exec 'pytest tests/ert/unit_tests -n logical -m "not integration_test"')

When applicable

• When there are user facing changes: Updated documentation
• New behavior or changes to existing untested code: Ensured that unit tests are added (See Ground Rules).
• Large PR: Prepare changes in small commits for more convenient review
• Bug fix: Add regression test for the bug
• Bug fix: Create Backport PR to latest release

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 91.85%. Comparing base (1889e2a) to head (b2662bd).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #9609      +/-   ##
==========================================
- Coverage   91.85%   91.85%   -0.01%     
==========================================
  Files         433      432       -1     
  Lines       26813    26791      -22     
==========================================
- Hits        24630    24609      -21     
+ Misses       2183     2182       -1     

Flag	Coverage Δ
cli-tests	39.74% <ø> (ø)
everest-models-test	34.60% <ø> (+<0.01%)	⬆️
gui-tests	72.12% <ø> (+0.01%)	⬆️
integration-test	38.73% <ø> (-0.02%)	⬇️
performance-tests	51.94% <ø> (ø)
test	40.03% <ø> (-0.06%)	⬇️
unit-tests	74.18% <ø> (+0.04%)	⬆️

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[codspeed-hq]

CodSpeed Performance Report

Merging #9609 will not alter performance

_{Comparing oyvindeide:remove_async (b2662bd) with main (1889e2a)}

Summary

✅ 24 untouched benchmarks