Tests: Remove deprecated `aiida/manage/tests/main` module and move system tests #3927

Job	Run time
validate-dependency-specification	10s
install-with-pip	26s
install-with-conda (3.9, true)	1m 49s
install-with-pip ([atomic_tools,docs,notebook,rest,tests,tui])	1m 32s
install-with-conda (3.10, true)	1m 13s
install-with-conda (3.11, true)	1m 8s
install-with-conda (3.12, true)	1m 19s
install-with-conda (false)	1m 17s
create-conda-environment	2m 42s
resolve-pip-dependencies (3.9)	1m 24s
resolve-pip-dependencies (3.10)	1m 25s
resolve-pip-dependencies (3.11)	1m 28s
resolve-pip-dependencies (3.12)	2m 35s
tests (3.9)	20m 52s
tests (3.10)	21m 36s
tests (3.11)	20m 14s
tests (3.12)	26m 24s
check-requirements	14s
	1h 47m 48s

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