Currently, I prefer the Kagi model as my daily driver – pay a small fee each month and not worry about having your search data, in all its forms, sold instead. They have some neat features, as well, like AI summaries and the ability to ask questions about pages. It’s those two features I have used to determine what kind of content, even musical, may be on the page for me without having to go to the page, itself.
There is also SearXNG, which is an open source, privacy-respecting, hackable metasearch engine. It can be self-hosted and also has a number of instances you can access.
+1 !!