Update `gen_coverage` and `gen_docs` to align with `build_locally` #5891

Job	Run time
build_linux (3.10)	33m 53s
build_linux (3.9)	33m 36s
build_windows (3.10)	43m 47s
build_windows (3.9)	46m 16s
build_windows (3.11)	44m 50s
build_linux (3.12)	35m 26s
build_windows (3.12)	43m 35s
build_linux (3.13)	34m 7s
build_windows (3.13)	46m 35s
build_linux (3.11)	33m 3s
test_examples_linux (3.11, false, ubuntu-22.04)	8m 29s
test_linux (3.9, false, ubuntu-22.04)	10m 53s
test_linux (3.10, false, ubuntu-22.04)	10m 23s
test_linux (3.11, false, ubuntu-22.04)	11m 25s
test_linux (3.13, false, ubuntu-22.04)	10m 15s
test_linux (3.12, false, ubuntu-22.04)	10m 34s
array-api-conformity (3.10, false, ubuntu-22.04)	5m 56s
test_windows (3.9, false, windows-latest)	14m 57s
test_windows (3.12, false, windows-latest)	14m 26s
test_windows (3.11, false, windows-latest)	14m 41s
test_windows (3.13, false, windows-latest)	13m 52s
test_windows (3.10, false, windows-latest)	15m 38s
upload_linux	0s
upload_windows	0s
Clean up anaconda packages	0s
	8h 56m 37s

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