Migrate to new `SerializableState` impls #1309

Job	Run time
minimal-versions / minimal-versions	1m 8s
set-msrv / set-msrv	4s
test (1.85.0)	1m 5s
build (stable, wasm32-unknown-unknown)	31s
build (stable, thumbv7em-none-eabi)	24s
build (1.85.0, wasm32-unknown-unknown)	30s
cross (1.85.0, aarch64-unknown-linux-gnu, default)	46s
build (1.85.0, thumbv7em-none-eabi)	24s
cross (stable, powerpc-unknown-linux-gnu, default)	48s
cross (stable, aarch64-unknown-linux-gnu, default)	42s
cross (1.85.0, powerpc-unknown-linux-gnu, default)	49s
test (stable)	1m 1s
	8m 12s

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