If you want to advertise your internal search engine (search engine of your website), you can do it:
Check the dedicated page: What is OpenSearch and how to use it?
Search Action is a potentialAction ld+json metadata 1)
Example:
{
"@context": "https://schema.org",
"@type": "WebSite",
"url": "https://www.example.com/",
"potentialAction": {
"@type": "SearchAction",
"target": "https://query.example.com/search?q={search_term_string}",
"query-input": "required name=search_term_string"
}
}