is there a link to the search api example?
doing
"permissions": ["search"]
in the manifest and

 chrome.search.query(
      { text: document.querySelector('input').value }
    ).then(e => console.log(e))

in my script returns
Cannot read properties of undefined (reading 'query')

Found the solution.
To be able to use the search api you also need to have permission to the tabs api.
so to fix my code all I had to do was modify my manifest to add
"permissions": ["tabs","search"]
If that information is mentioned anywhere in the search api reference Im blind cause I didnt saw it.

I'm not sure why this was closed, since we don't have a search example.

cc: @patrickkettner

I would like to write a sample for this!

My idea is the following: clicking on the extension icon a popup will appear, from there you can type the search query and choose where it should be opened (current tab, new tab etc.).

Thanks @Pask00, that sounds like a good plan. I'll assign you to this issue.