Make SSE less dependent on tokio #5239

Job	Run time
check-docs	12s
check	36s
cargo-hack	28s
cargo-public-api-crates (axum)	55s
cargo-public-api-crates (axum-core)	35s
cargo-deny check (advisories)	21s
dependencies-are-sorted	13s
cargo-public-api-crates (axum-extra)	45s
Spell Check with Typos	3s
cargo-deny check (bans licenses sources)	25s
cargo-public-api-crates (axum-macros)	38s
test-docs	1m 29s
test-msrv	2m 40s
test-nightly	1m 11s
armv5te-unknown-linux-musleabi	25s
test-versions (stable)	1m 12s
wasm32-unknown-unknown	15s
test-versions (beta)	1m 13s
	13m 36s

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