Show project picker before auth/waiting-room gates #6216

Job	Run time
build-and-check	3m 8s
test-integration-packages/internal	1m 9s
test-integration-packages/billing	1m 4s
test-integration-web	50s
test-integration-packages/agent-runtime	53s
test-integration-cli	51s
test-integration-common	52s
test-integration-sdk	1m 23s
test-packages/agent-runtime	54s
test-sdk	48s
test-packages/billing	47s
test-packages/internal	49s
test-web	1m 5s
test-cli	54s
test-.agents	45s
test-common	43s
	16m 55s

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