Upgrade-5: `prover` Refactor #8172

Job	Run time
skip_check	5s
Intra-doc links	6m 3s
Rustfmt	3m 46s
Bitrot check	0s
Build target ${{ matrix.target }}	0s
TyposCheck	6s
runner / select	1s
runner / Wake up self-hosted runner	41s
Test Default	0s
Test Scroll (jenkins2)	26m 24s
	37m 6s

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