[release-16.0] Don't run any reparent commands if the host is empty (#13396)

[GuptaManan100]

Description

This is a backport of #13396

[vitess-bot]

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[deepthi]

Upgrade/Downgrade test is failing. I've seen this type of failure several times but I can't recall whether it is flakiness that goes away on re-run. It's worth at least examining the failure before re-trying.
EDIT: This actually ran 3 times and failed all 3 times.

[GuptaManan100]

@deepthi This test has been failing on other release-16.0 backports too. I'll investigate it separately.

[GuptaManan100]

Found the bug - #13407 and the fix - #13408