Update `gen_coverage` and `gen_docs` to align with `build_locally` #5849

Job	Run time
build_windows (3.11)	41m 34s
build_windows (3.9)	43m 42s
build_linux (3.11)	34m 24s
build_windows (3.12)	40m 6s
build_windows (3.10)	36m 48s
build_linux (3.12)	33m 55s
build_linux (3.10)	35m 43s
build_linux (3.9)	35m 7s
build_windows (3.13)	41m 9s
build_linux (3.13)	34m 59s
test_examples_linux (3.11, false, ubuntu-22.04)	8m 24s
array-api-conformity (3.10, false, ubuntu-22.04)	4m 57s
test_linux (3.9, false, ubuntu-22.04)	11m 2s
test_linux (3.12, false, ubuntu-22.04)	10m 44s
test_linux (3.10, false, ubuntu-22.04)	10m 17s
test_linux (3.13, false, ubuntu-22.04)	12m 31s
test_linux (3.11, false, ubuntu-22.04)	10m 25s
test_windows (3.10, false, windows-latest)	14m 38s
test_windows (3.11, false, windows-latest)	12m 37s
test_windows (3.13, false, windows-latest)	14m 4s
test_windows (3.9, false, windows-latest)	14m 26s
test_windows (3.12, false, windows-latest)	14m 54s
upload_linux	0s
Clean up anaconda packages	0s
upload_windows	0s
	8h 36m 26s

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