Update `gen_coverage` and `gen_docs` to align with `build_locally` #5884

Job	Run time
build_linux (3.12)	34m 0s
build_linux (3.11)	34m 14s
build_windows (3.12)	44m 5s
build_linux (3.9)	35m 3s
build_linux (3.13)	34m 9s
build_windows (3.11)	44m 22s
build_windows (3.9)	43m 57s
build_windows (3.13)	41m 11s
build_windows (3.10)	44m 17s
build_linux (3.10)	35m 54s
test_examples_linux (3.11, false, ubuntu-22.04)	11m 50s
test_linux (3.9, false, ubuntu-22.04)	11m 14s
array-api-conformity (3.10, false, ubuntu-22.04)	4m 41s
test_linux (3.12, false, ubuntu-22.04)	11m 34s
test_linux (3.10, false, ubuntu-22.04)	12m 31s
test_linux (3.13, false, ubuntu-22.04)	10m 21s
test_linux (3.11, false, ubuntu-22.04)	12m 55s
test_windows (3.10, false, windows-latest)	12m 58s
test_windows (3.9, false, windows-latest)	16m 49s
test_windows (3.13, false, windows-latest)	14m 56s
test_windows (3.12, false, windows-latest)	13m 16s
test_windows (3.11, false, windows-latest)	14m 50s
upload_linux	0s
upload_windows	0s
Clean up anaconda packages	0s
	8h 59m 7s

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