client/v3 fix watch API blocked forever even with `WithRequireLeader` option #12523

Job	Run time
arm64 / test (linux-arm64-integration-1-cpu)	16m 20s
amd64 / test (linux-amd64-integration-1-cpu)	14m 24s
arm64 / test (linux-arm64-integration-2-cpu)	17m 6s
amd64 / test (linux-amd64-integration-2-cpu)	8m 41s
arm64 / test (linux-arm64-integration-4-cpu)	16m 48s
amd64 / test (linux-amd64-integration-4-cpu)	13m 46s
amd64 / test (linux-amd64-unit-4-cpu)	4m 34s
arm64 / test (linux-arm64-unit-4-cpu)	6m 8s
amd64 / test (linux-386-unit-1-cpu)	2m 6s
arm64 / test (linux-386-unit-1-cpu)	15s
	1h 40m 8s

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