Make SSE less dependent on tokio #5240

Job	Run time
check	41s
cargo-public-api-crates (axum)	55s
cargo-public-api-crates (axum-core)	37s
check-docs	12s
cargo-hack	3m 6s
cargo-deny check (advisories)	25s
cargo-public-api-crates (axum-extra)	45s
cargo-deny check (bans licenses sources)	22s
cargo-public-api-crates (axum-macros)	39s
dependencies-are-sorted	14s
Spell Check with Typos	3s
test-docs	1m 21s
test-versions (stable)	1m 25s
test-msrv	2m 47s
armv5te-unknown-linux-musleabi	26s
test-nightly	1m 11s
wasm32-unknown-unknown	10s
test-versions (beta)	1m 19s
	16m 38s

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