Add StartupTimings per-phase breakdown to Client::start #1875

Job	Run time
Rust SDK Tests (ubuntu-latest, inprocess)	12m 45s
Rust SDK Tests (ubuntu-latest, default)	10m 23s
Rust SDK Tests (macos-latest, default)	6m 54s
Rust SDK Bundled CLI Build (windows-latest)	4m 26s
Rust SDK Tests (macos-latest, inprocess)	15m 32s
Rust SDK Bundled CLI Build (macos-latest)	3m 35s
Rust SDK Bundled CLI Build (ubuntu-latest)	3m 18s
Rust SDK Tests (windows-latest, default)	13m 1s
	1h 9m 54s

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