[main] Stats Flags: include stats flags in the correct binaries (#11450)

[vitess-bot]

Description

This is a forwardport of #11450.

[vitess-bot]

Review Checklist

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[deepthi]

can ignore web test failure for now, it's flaky, and we are going to delete it in a couple of weeks.

[rohit-nayak-ps]

lgtm