I compiled a list of search engines that use their own indexes for organic results: https://seirdy.one/2021/03/10/search-engines-with-own-indexes.html

I typically use a Searx/SearxNG instance that mixes Google, Bing, and Bing-derivatives (e.g. DDG) with other indexes: petal, Mojeek, Gigablast, and Qwant (Qwant mixes its own results with Bing’s).

I’ll probably post a big update to that article at some point that compares if/how some of the listed engines process structured data.