There are 2 templates being used for result, one for simple search ( using top search field ) and other is for advance search field :

For Top search field result :

module_catalog-search/view/frontend/templates/result.phtml

For Advance Search result :

module_catalog-search/view/frontend/templates/advanced/result.phtml

And both search fields search data / record within product catalog, override the template(s), and add your condition in that template to show whatever data you want to show if there is no record is returned.

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