chore: remove use of state field in SpanBuilder #278

Job	Run time
cargo check	43s
cargo check (feature combinations)	22s
cargo check (+MSRV -Zminimal-versions) (1.75.0)	30s
cargo check (+MSRV -Zminimal-versions) (stable)	29s
cargo fmt	17s
warnings	44s
build tests (wasm32-unknown-unknown)	59s
cargo test (stable on ubuntu-latest)	1m 2s
build tests (wasm32-wasip1)	1m 0s
cargo test (nightly on ubuntu-latest)	56s
cargo test (beta on ubuntu-latest)	58s
cargo test (stable on macos-latest)	1m 10s
cargo test (stable on windows-latest)	1m 56s
all systems go!	2s
	11m 8s

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