Fix race condition that prevents queries from being buffered after vtgate startup #896

Job	Run time
Set push variable	1s
Build and push vttestserver (mysql80)	1m 59s
Build and push lite (latest)	2m 12s
Build and push lite (percona80)	2m 17s
Build and push (bullseye, vtadmin)	1m 19s
Build and push (bullseye, vtorc)	27s
Build and push (bullseye, vtgate)	42s
Build and push (bullseye, vttablet)	35s
Build and push (bullseye, mysqlctld)	41s
Build and push (bullseye, mysqlctl)	36s
Build and push (bullseye, vtctl)	43s
Build and push (bullseye, vtctlclient)	39s
Build and push (bullseye, vtctld)	1m 3s
Build and push (bullseye, vtctldclient)	39s
Build and push (bullseye, logrotate)	26s
Build and push (bullseye, logtail)	15s
Build and push (bullseye, vtbackup)	29s
Build and push (bullseye, vtexplain)	23s
Build and push (bookworm, vtadmin)	1m 15s
Build and push (bookworm, vtorc)	42s
Build and push (bookworm, vtgate)	40s
Build and push (bookworm, vttablet)	34s
Build and push (bookworm, mysqlctld)	37s
Build and push (bookworm, mysqlctl)	44s
Build and push (bookworm, vtctl)	31s
Build and push (bookworm, vtctlclient)	30s
Build and push (bookworm, vtctld)	1m 2s
Build and push (bookworm, vtctldclient)	30s
Build and push (bookworm, logrotate)	25s
Build and push (bookworm, logtail)	25s
Build and push (bookworm, vtbackup)	46s
Build and push (bookworm, vtexplain)	33s
	24m 40s

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