There are search engines that claim not to track and collect user data. At the same time, you can't be 100% sure of that. For example, search engines can also store user data to improve the quality of the search engine itself. If you want to be sure, the advice is to read the privacy statement of the search engine you use. One of the search engines that focuses on privacy is DuckDuckGo. They state that they do not share or store users' search data. Other (somewhat less known) search engines that are a safer choice in terms of privacy are Qwant and StartPage.