refactor(cli/self-update): move `process` out of `InstallOpts` #5185

Job	Run time
build-macos-aarch64 (dev, aarch64-apple-darwin)	5m 20s
build-linux-pr (dev, aarch64-unknown-linux-gnu)	5m 16s
build-windows-pr (dev, x86_64-pc-windows-gnu)	5m 7s
build-macos-x86_64 (release, x86_64-apple-darwin)	5m 17s
build-macos-x86_64 (dev, x86_64-apple-darwin)	5m 27s
build-windows-pr (dev, x86_64-pc-windows-msvc)	5m 14s
build-macos-aarch64 (release, aarch64-apple-darwin)	5m 19s
build-linux-pr (release, aarch64-unknown-linux-gnu)	4m 33s
doc	10s
build-windows-pr (release, aarch64-pc-windows-msvc)	5m 15s
build-linux-pr (release, aarch64-linux-android)	5m 16s
build-linux-pr (dev, x86_64-unknown-linux-gnu)	5m 16s
build-linux-pr (dev, armv7-unknown-linux-gnueabihf)	3m 59s
build-windows-pr (dev, aarch64-pc-windows-msvc)	5m 16s
build-windows-pr (dev, aarch64-pc-windows-gnullvm)	5m 9s
build-all-features (ubuntu-latest, x86_64-unknown-linux-gnu)	5m 14s
build-linux-pr (dev, aarch64-linux-android)	3m 43s
check	3m 2s
build-all-features (windows-latest, x86_64-pc-windows-msvc)	5m 6s
build-windows-pr (release, x86_64-pc-windows-msvc)	5m 13s
build-windows-pr (release, aarch64-pc-windows-gnullvm)	5m 16s
build-linux-pr (release, armv7-unknown-linux-gnueabihf)	5m 16s
build-linux-pr (release, x86_64-unknown-linux-gnu)	5m 15s
build-windows-pr (release, x86_64-pc-windows-gnu)	5m 14s
build-windows-main	0s
build-linux-stable	0s
build-windows-stable	0s
build-freebsd-stable	0s
build-freebsd-main	0s
build-linux-main	0s
conclusion	3s
	1h 55m 16s

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