For example, the first search result on this page leads to the older SO question, with the following HTTP request:
GET /questions/4402502/how-does-google-set-the-http-referrer-when-someone-clicks-on-a-search-result-lin HTTP/1.1
Host stackoverflow.com
Referer https://www.google.ru
Note, that:
The question is, how do they achieve this?
Google makes use of Referrer Policy. They include the meta tag in the page:
<meta name="referrer" content="origin">
This tells browsers to use "Origin Only" policy, that is, to send domain only information in the Referrer header in any subsequent request.