Add StartupTimings per-phase breakdown to Client::start #1873

Job	Run time
Rust SDK Tests (macos-latest, default)	7m 30s
Rust SDK Tests (ubuntu-latest, default)	8m 31s
Rust SDK Tests (macos-latest, inprocess)	16m 4s
Rust SDK Bundled CLI Build (windows-latest)	4m 22s
Rust SDK Bundled CLI Build (macos-latest)	4m 9s
Rust SDK Tests (windows-latest, default)	13m 32s
Rust SDK Tests (ubuntu-latest, inprocess)	14m 40s
Rust SDK Bundled CLI Build (ubuntu-latest)	3m 21s
	1h 12m 9s

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