I've taken to using Kagi. It may not meet your privacy requirements (more below), but it does keep the web wonderfully shopping mall free. It's a paid search engine, it sources results anonymously from other search engines as well as its having its own internal database. I generally find because the search results are weighted by its own criteria which in no way is influenced by ad revenue decisions they tend to be pretty good -- plus you can customize them by assigning your own weightings to sources you like to use a lot (like, say, Wikipedia) or ones you never want to see (like AI-generated spam domains). Privacy may be where it breaks down for you, and will depend on your threat model. For the most part, my privacy concerns are more for private businesses and advertisers -- which it excels at protecting me again. If I was concerned about law-enforcement it may be less desirable (it is run out of the USA and is presumably subject to subpoena), likewise for state-level espionage (and if that's your concern, you wouldn't be asking this question anyway).

All in all, hugely happy with it and totally think I've gotten my money's worth from it -- but I also totally get a lot of people aren't interested or are unable to pay for a search engine. I figure I'm paying one way or another, and I'd far rather pay this way than with my time sorting through ad spam. If you are interested, they have a tonne of documentation explaining their philosophy, search results, privacy policy, and what all you get for your money.

DDG proxies Bing results with extra privacy. Startpage proxies Google results with extra privacy (it's a bit slow in my opinion though).

Ecosia proxies both with a bit oft extra privacy, as long as you don't click or block the advertised results.

SearX proxies whatever you want, but its kinda slow last time I tried it.

Brave Search builds their own index, which is pretty good (on par with Bing) even though they're only about a year old at this point. The company is a bit sketchy though.

Searx is pretty good, but you have to tell it to use search engines. It uses cookies to store settings by default, but they expire in about a month. You can also use a URL that stores the configuration, or good old !bangs. For example, !go will return results from Google - and it doesn't compromise privacy since the Searx instance is the one making the query to Google, and then it passes the results to you.

I like Qwant. It advertises being privacy based, I guess I don't know just how private but it provides me better results than DDG did.

https://librey.devol.it

If you like it you might go into settings and change it to prefer search results in your language since I think it defaults to Italian.

DuckDuckGo. I also used to use Starting Page although it's been a while.

Startpage if you want proxied google results.

Torch