Fix potential deadlock in health streamer (#17261) #447

Job	Run time
Build and push lite (latest)	4m 25s
Build and push vttestserver (mysql80)	2m 25s
Build and push lite (percona80)	4m 40s
Build and push (bullseye, vtadmin)	1m 30s
Build and push (bullseye, vtorc)	44s
Build and push (bullseye, vtgate)	48s
Build and push (bullseye, vttablet)	46s
Build and push (bullseye, mysqlctld)	52s
Build and push (bullseye, mysqlctl)	57s
Build and push (bullseye, vtctl)	54s
Build and push (bullseye, vtctlclient)	40s
Build and push (bullseye, vtctld)	1m 30s
Build and push (bullseye, vtctldclient)	44s
Build and push (bullseye, logrotate)	29s
Build and push (bullseye, logtail)	32s
Build and push (bullseye, vtbackup)	55s
Build and push (bullseye, vtexplain)	39s
Build and push (bookworm, vtadmin)	1m 33s
Build and push (bookworm, vtorc)	46s
Build and push (bookworm, vtgate)	49s
Build and push (bookworm, vttablet)	44s
Build and push (bookworm, mysqlctld)	55s
Build and push (bookworm, mysqlctl)	38s
Build and push (bookworm, vtctl)	59s
Build and push (bookworm, vtctlclient)	59s
Build and push (bookworm, vtctld)	1m 41s
Build and push (bookworm, vtctldclient)	48s
Build and push (bookworm, logrotate)	44s
Build and push (bookworm, logtail)	49s
Build and push (bookworm, vtbackup)	45s
Build and push (bookworm, vtexplain)	41s
Slack Notification if failed	0s
	36m 21s

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