Update `gen_coverage` and `gen_docs` to align with `build_locally` #5882

Job	Run time
build_linux (3.10)	33m 33s
build_windows (3.9)	44m 32s
build_windows (3.13)	44m 1s
build_windows (3.10)	45m 30s
build_windows (3.12)	42m 43s
build_linux (3.9)	31m 55s
build_linux (3.12)	35m 8s
build_linux (3.13)	33m 55s
build_windows (3.11)	45m 9s
build_linux (3.11)	33m 18s
test_linux (3.13, false, ubuntu-22.04)	10m 44s
test_examples_linux (3.11, false, ubuntu-22.04)	10m 29s
array-api-conformity (3.10, false, ubuntu-22.04)	5m 12s
test_linux (3.12, false, ubuntu-22.04)	10m 50s
test_linux (3.10, false, ubuntu-22.04)	10m 48s
test_linux (3.11, false, ubuntu-22.04)	10m 39s
test_linux (3.9, false, ubuntu-22.04)	10m 48s
test_windows (3.9, false, windows-latest)	14m 44s
test_windows (3.13, false, windows-latest)	14m 45s
test_windows (3.10, false, windows-latest)	15m 18s
test_windows (3.11, false, windows-latest)	13m 48s
test_windows (3.12, false, windows-latest)	15m 22s
upload_linux	0s
Clean up anaconda packages	0s
upload_windows	0s
	8h 53m 11s

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