Try Andisearch, it was the first AI search ever and apart is one of the most private search engine which even actively protect your ID, no ads, no tracking, no logs, anonymous.

Adding as search engine in your browser

https://andisearch.com/?query=%s

Perplexity, well, is still one of the more private AI, but best to use the extension which works well and anonymous (logs only tech data), Chromium only. In Firefox you can use perplexity only as search engine from the website itself.