Currently you can enable to hide the referrer (& therefore the search query). However this is ugly as redirections need time and right-clicking on a search result won't give you the correct link and all in all it is a quite outdated behaviour.
And there are better modern an unobtrusive alternatives. To name them:
1. Use Content Security Policy
I'd suggest you anyway) and include `referrer no-referrer;` there, which makes recent browsers to ignore the referrer.
2. Use a Referrer Policy: https://w3c.github.io/webappsec-referrer...
This can be done as a HTML meta tag (with good browser support) or a HTTP header (less browser support).
Personally I'd just suggest you to combine these two methods.
More information can be found on this test site: https://webbkoll.dataskydd.net/en