Upgrade-5: `prover` Refactor #8173

Job	Run time
skip_check	5s
Build target ${{ matrix.target }}	0s
Bitrot check	0s
Intra-doc links	1m 6s
Rustfmt	1m 4s
TyposCheck	6s
runner / select	1s
runner / Wake up self-hosted runner	54s
Test Default	1s
Test Scroll	1s
	3m 18s

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