Add basic telemetry for `start-proxy` Action #5887

Job	Run time
Ruby analysis (macos-latest, default)	1s
Ruby analysis (ubuntu-latest, default)	50s
Ruby analysis (macos-latest, linked)	1s
Ruby analysis (macos-latest, nightly-latest)	1s
Ruby analysis (ubuntu-latest, linked)	48s
Ruby analysis (ubuntu-latest, nightly-latest)	54s
Ruby analysis (macos-latest, linked)	1m 11s
Ruby analysis (ubuntu-latest, linked)	48s
Ruby analysis (macos-latest, default)	51s
Ruby analysis (ubuntu-latest, default)	50s
Ruby analysis (macos-latest, nightly-latest)	1m 0s
Ruby analysis (ubuntu-latest, nightly-latest)	54s
	8m 9s

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