I use kagi. I think it depends on your level of concern , as it does with most things. Kagi has a pretty nicely written privacy policy. They do require an account but I signed up with a masked email and cc. For my use I find their privacy policy enough given the other measures I take but the main reason I like kagi is zero ads or prioritized posting. Experiencing search with out ads is a pretty awesome exp in my opinion. There are other ways to get free search with ads stripped out but this “feel” fundamentally different from a service purpose built to be ad free and private. I am happy to pay for ad free platforms vs using platforms that are trying to do privacy preserving ads but this is more of a personal stance and preference. I know your question was more about privacy than ads but I find the two closely linked. I’ve attached a summary of their privacy policy below:

• Searches are anonymous and private to you. Kagi does not see what you are searching at all.
• We do not log or store your IP address. Your IP address is used only temporarily when enriching location/maps searches, and is not shared with any other party.
• We only store cookies needed for site functionality. We do not use any web browser analytics or other frontend telemetry.
• We do not display any ads, or have any first-party or third-party tracking in service of ads.
• We do not share customer data with third parties, except as needed to perform explicitly accessed services. In those cases, we will share the minimum amount of data needed to provide the service, and will do so in an anonymous way.
• We collect only the data needed to provide and protect the service.
• We proxy all images to prevent tracking from third parties.
• We use HTTPS encryption everywhere. All passwords are hashed and salted.

https://kagi.com/privacy