Updated authentication process for `gam print|show projects`. #3676

Job	Run time
build (ubuntu-22.04, 1, build, x86_64, linux-x86_64)	15m 4s
build (ubuntu-24.04, 2, build, x86_64, linux-x86_64)	18m 2s
build (self-hosted, linux, arm64, 3, build, aarch64, linux-aarch64)	18m 17s
build (ubuntu-22.04, 4, build, x86_64, linux-x86_64, yes)	17m 48s
build (self-hosted, linux, arm64, 5, build, aarch64, linux-aarch64, yes)	18m 49s
build (macos-13, 6, build, x86_64, darwin64-x86_64)	17m 28s
build (macos-14, 7, build, aarch64, darwin64-arm64)	16m 41s
build (windows-2022, 8, build, Win64, VC-WIN64A)	19m 29s
build (ubuntu-24.04, test, 3.9, 9, x86_64)	15m 23s
build (ubuntu-24.04, test, 3.10, 10, x86_64)	18m 33s
build (ubuntu-24.04, test, 3.11, 11, x86_64)	14m 33s
build (ubuntu-24.04, test, 3.12, 12, x86_64)	14m 37s
merge	10s
publish	4m 30s
	3h 29m 24s

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