Migrate to new `SerializableState` impls #1310

Job	Run time
minimal-versions / minimal-versions	1m 2s
set-msrv / set-msrv	3s
build (1.85.0, wasm32-unknown-unknown)	31s
build (1.85.0, thumbv7em-none-eabi)	23s
test (stable)	1m 4s
build (stable, thumbv7em-none-eabi)	24s
test (1.85.0)	57s
cross (1.85.0, aarch64-unknown-linux-gnu, default)	1m 26s
cross (stable, aarch64-unknown-linux-gnu, default)	1m 20s
cross (1.85.0, powerpc-unknown-linux-gnu, default)	37s
build (stable, wasm32-unknown-unknown)	1m 38s
cross (stable, powerpc-unknown-linux-gnu, default)	1m 13s
	10m 38s

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