Backport of test: fix flakey broker notifier test. into release/1.5.x #17136
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Backport
This PR is auto-generated from #16994 to be assessed for backporting due to the inclusion of the label backport/1.5.x.
The below text is copied from the body of the original PR.
The test had a race condition which meant some subcribers would not be setup by the time the test sent the notification. This would mean the subcribers would timeout, rather than receive the message and cause failure. This change updates the test to avoid this.