Provide `Authorization` header when downloading `update-job-proxy` #5802

Job	Run time
Go: tracing with custom build steps (macos-latest, stable-v2.17.6)	2m 56s
Go: tracing with custom build steps (ubuntu-latest, stable-v2.18.4)	1m 20s
Go: tracing with custom build steps (macos-latest, stable-v2.18.4)	2m 29s
Go: tracing with custom build steps (macos-latest, default)	3m 4s
Go: tracing with custom build steps (ubuntu-latest, stable-v2.17.6)	1m 13s
Go: tracing with custom build steps (ubuntu-latest, stable-v2.22.4)	1m 9s
Go: tracing with custom build steps (ubuntu-latest, stable-v2.19.4)	1m 17s
Go: tracing with custom build steps (ubuntu-latest, linked)	58s
Go: tracing with custom build steps (macos-latest, stable-v2.21.4)	2m 20s
Go: tracing with custom build steps (ubuntu-latest, stable-v2.21.4)	1m 10s
Go: tracing with custom build steps (macos-latest, linked)	2m 19s
Go: tracing with custom build steps (macos-latest, nightly-latest)	2m 39s
Go: tracing with custom build steps (macos-latest, stable-v2.19.4)	2m 56s
Go: tracing with custom build steps (ubuntu-latest, default)	52s
Go: tracing with custom build steps (macos-latest, stable-v2.22.4)	2m 39s
Go: tracing with custom build steps (macos-latest, stable-v2.20.7)	2m 52s
Go: tracing with custom build steps (ubuntu-latest, nightly-latest)	1m 5s
Go: tracing with custom build steps (ubuntu-latest, stable-v2.20.7)	1m 19s
	34m 37s

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