Remove unused function async_session in dark storage #15185

Job	Run time
Test ert docs (3.12, ubuntu-latest)	1m 4s
build-wheels (3.11) / build-wheels	13s
build-wheels (3.12) / build-wheels	12s
test-ert-with-flow (ubuntu-latest, 3.11) / Run ert tests	9m 45s
test-linux-ert (cli-tests, 3.12, ubuntu-latest) / Run ert tests	16m 37s
test-linux-ert (gui-tests, 3.11, ubuntu-latest) / Run ert tests	11m 13s
test-linux-ert (cli-tests, 3.11, ubuntu-latest) / Run ert tests	14m 7s
test-linux-ert (gui-tests, 3.12, ubuntu-latest) / Run ert tests	13m 41s
test-linux-ert (performance-and-unit-tests, 3.12, ubuntu-latest) / Run ert tests	9m 26s
test-linux-ert (performance-and-unit-tests, 3.11, ubuntu-latest) / Run ert tests	8m 5s
test-linux-everest (everest-models-test, 3.11, ubuntu-latest) / Run everest tests	1m 47s
test-linux-everest (doc, 3.12, ubuntu-latest) / Run everest tests	48s
test-linux-everest (everest-models-test, 3.12, ubuntu-latest) / Run everest tests	2m 3s
test-linux-everest (test, 3.11, ubuntu-latest) / Run everest tests	7m 11s
test-linux-everest (test, 3.12, ubuntu-latest) / Run everest tests	8m 27s
test-mac-main-ert (cli-tests, 3.12, macos-latest) / Run ert tests	14m 24s
test-mac-main-ert (gui-tests, 3.12, macos-latest) / Run ert tests	11m 10s
test-mac-main-ert (performance-and-unit-tests, 3.12, macos-latest) / Run ert tests	8m 3s
test-mac-main-everest (everest-models-test, macos-latest, 3.12) / Run everest tests	1m 48s
test-mac-main-everest (test, macos-latest, 3.12) / Run everest tests	6m 32s
test-slurm (ubuntu-latest, 3.11) / Run ert tests	1m 50s
Publish to PyPI	0s
	2h 28m 26s

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