refactor(pkg): inline process_dep #29438

Job	Run time
Format	1m 7s
Nix (macos-latest)	1m 55s
Documentation	55s
Build (macos-latest, 5.1.x)	14m 30s
Nix (ubuntu-latest)	57s
Build (ubuntu-latest, 5.1.x)	8m 31s
Build microbenchmarks	2m 36s
Build (ocaml-variants.5.3.0+trunk, ubuntu-latest, true)	1m 34s
Coq 8.16.1	7m 11s
Build (4.14.x, ubuntu-latest, true)	1m 28s
Create local opam switch (macos-latest, 5)	5m 34s
Build (4.14.x, macos-latest, true)	2m 14s
Create local opam switch (macos-latest, 4.14)	5m 54s
Build monorepo benchmark docker image	3m 41s
Wasm_of_ocaml	10m 18s
Build (5.1.x, macos-13, true)	4m 13s
Create local opam switch (ubuntu-latest, 5)	5m 1s
Build (ocaml-base-compiler.4.14.2,system-msvc, windows-latest)	14m 29s
Create local opam switch (ubuntu-latest, 4.14)	4m 59s
Build (ocaml-base-compiler.5.1.1,system-mingw, windows-latest)	8m 19s
Build (4.08.x, ubuntu-latest, true)	1m 28s
Build (4.04.x, ubuntu-latest, true, true)	4m 26s
Build (4.02.x, ubuntu-latest, true)	3m 59s
	1h 55m 19s

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