fix: save key name mapping verifies if there is a client running (#244) [backport] #541

Job	Run time
docker_pipeline / prepare-metadata	1s
lint_test / build	32s
lint_test / gosec	2m 42s
lint_test / check-mock-gen	0s
lint_test / integration-tests	9m 48s
lint_test / unit-tests	57s
lint_test / lint	37s
docker_pipeline / docker_build (linux/amd64, ubuntu-24.04)	3m 14s
docker_pipeline / docker_build (linux/arm64, ubuntu-24.04-arm64)	3m 19s
docker_pipeline / merge_ecr	0s
docker_pipeline / merge_dockerhub	0s
	21m 10s

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