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.
Remember that time you realized it was possible to refresh your Jira data in Google sheets with just one click? What if we told you that you can now get the latest data with no clicks at all?! Zero! ...
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