Remove duplication in serving with and without graceful shutdown #4769

Job	Run time
check	46s
cargo-hack	3m 13s
check-docs	14s
cargo-public-api-crates (axum)	29s
cargo-public-api-crates (axum-core)	17s
cargo-deny check (advisories)	24s
dependencies-are-sorted	13s
Spell Check with Typos	4s
cargo-public-api-crates (axum-extra)	29s
cargo-public-api-crates (axum-macros)	19s
cargo-deny check (bans licenses sources)	24s
test-nightly	1m 6s
test-msrv	1m 0s
armv5te-unknown-linux-musleabi	20s
test-docs	1m 31s
test-versions (stable)	1m 9s
test-versions (beta)	1m 17s
wasm32-unknown-unknown	18s
	13m 33s

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