It is possible to search for checklist items by assigned/mentioned users with Jira’s JQL search.
Search by currently logged user
Go to Advanced issue search and type:
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The JQ: search will return all Jira issues with assignees mentioned in checklist items
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Search by any user
issue.property[SmartChecklist].assignees ~ 557058:92eea4c7-8696-447f-9d05-b625db07be7f
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