It is the question behind a lot of search-privacy worry: are they selling my data? The honest answer is more specific than a yes or no. Most large engines do not hand your search list to a buyer. They do something that often feels worse.
What "selling your data" usually means
The big engines rarely sell raw search logs to outsiders. Instead, they keep the data and rent access to your attention. Advertisers do not get your searches, they get to put a message in front of the profile your searches helped build. Your information stays in-house and becomes the engine's most valuable asset.
How search-based ads actually work
There are two broad models. Behavioral advertising targets you based on a history of everything you have searched and visited. Contextual advertising targets only the words in your current query, with no profile involved. The first needs to remember you. The second does not.
The version with no profile
Bare is built so the profile never exists in the first place. There is no account, no search history, and no behavioral tracking, so there is nothing to sell, rent, or leak. Your query passes through our server only to fetch results, and is gone once the page loads.
If sponsored or affiliate links ever appear, they are clearly labeled and matched only to the words in your current search, never to a profile of you. The funding model is contextual by design, not behavioral, and ignoring those links changes nothing about your results.
The simplest protection
You cannot audit what a giant company does with its logs, but you can choose not to feed them. Searching on an engine that keeps no profile means there is no data to sell, by anyone, ever. That is the cleanest answer to the whole question.