There is no such thing as a "multiple assignee" in Jira - it deliberately has a single-value assignee field to avoid all the avoidable problems with multiple assignees.
The gadget is therefore coded to look only at the single assignee field.
I suspect one of your admins has decided to cause problems by adding a custom "multiple assignee" field. The closest you can get to the "assigned to me" gadget is to create your own "filter results" gadget that looks at the custom field.
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