archive: Refactor `archive_storage` method into subscription #15001

Job	Run time
check-dependency-rules	9s
check-fail-ci	26s
check-markdown	18s
check-readme	3m 4s
check-workspace	14s
preflight / preflight	44s
preflight / ci-versions	1m 0s
check-rust-feature-propagation	2m 9s
check-toml-format	1m 9s
check-umbrella	2m 32s
fmt	1m 12s
test-rust-features	2m 12s
All quick checks passed	1s
	15m 10s

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