[Backport] [v16] Purge logs without panicking (#12187)

[ajm188]

Description

This back ports #12187 to release-16.0

Related Issue(s)

Checklist

• "Backport to:" labels have been added if this change should be back-ported
• Tests were added or are not required
• Did the new or modified tests pass consistently locally and on the CI
• Documentation was added or is not required

Deployment Notes

[vitess-bot]

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