I have made a website with HTML CSS and JavaScript that has a search engine at /search?q=(search query) (engine explaned here and here) and I want the browser to know that my website has it, for example, when you visit any stack exchange community, when you write down the url it shows a search option on google chrome, no need of manual user setup... how can I do this for my website?
I searched on google, but no results were found...
Google the following: google search results search box
First result: https://developers.google.com/search/docs/advanced/structured-data/sitelinks-searchbox
Google Search may automatically expose a search box scoped to your website when it appears as a search result, without you having to do anything additional to make this happen. This search box is powered by Google Search. However, you can explicitly provide information by adding WebSite structured data, which can help Google better understand your site.
Check other results too.