@AnuragSingh-MSFT - Thanks for reaching out to us.
The log search query needs to be modified to ensure it stays within the size limit. This can be achieved by either reducing the size of the current query or splitting it into separate alerts to meet different monitoring requirements. By adjusting the query accordingly, you should be able to update the alert rule successfully without encountering the error.
For more information on creating and managing alert rules in Azure, please refer to this doc: Azure Monitor documentation.
Hope this helps. and please feel free to reach out if you have any further questions.
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