refactor(client): de-duplicate process & run and split into h3 & h09 #1818

Job	Run time
Build & test (ubuntu-latest, 1.74.0, debug)	7m 6s
Build & test (ubuntu-latest, 1.74.0, debug)	7m 6s
Build & test (ubuntu-latest, stable, debug)	6m 6s
Build & test (ubuntu-latest, stable, debug)	7m 46s
Build & test (ubuntu-latest, nightly, debug)	7m 14s
Build & test (ubuntu-latest, nightly, debug)	7m 14s
Build & test (macos-14, 1.74.0, debug)	8m 38s
Build & test (macos-14, 1.74.0, debug)	8m 38s
Build & test (macos-14, stable, debug)	8m 44s
Build & test (macos-14, stable, debug)	8m 44s
Build & test (macos-14, nightly, debug)	9m 37s
Build & test (macos-14, nightly, debug)	9m 37s
Build & test (windows-latest, 1.74.0, debug)	17m 9s
Build & test (windows-latest, 1.74.0, debug)	17m 9s
Build & test (windows-latest, stable, debug)	16m 30s
Build & test (windows-latest, stable, debug)	16m 30s
Build & test (windows-latest, nightly, debug)	15m 41s
Build & test (windows-latest, nightly, debug)	15m 41s
Build & test (ubuntu-latest, stable, release)	8m 46s
Build & test (ubuntu-latest, stable, release)	8m 46s
Benchmark	0s
Benchmark / Benchmark	6m 32s
	3h 39m 14s

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