Because of this only a few search engines do so, if we exclude Asia the only starch engines I know which do so are Google, bing and Yandex(?).
All other defer to one of thos search engines (most times bing) while decoupling, post and pre processing queries to a varying degree.
Generally I would avoid Brave as the company behind is is quite doggy.
> if we exclude Asia the only starch engines I know which do so are Google, bing and Yandex(?).
Asia...and Europe? I'm pretty sure that for example Seznam.cz still has its own indexing (https://blog.seznam.cz/en/history-of-web-search/). At the very least there used to be several more indexers as well. A version of one them is even accessible as source code: https://www.ucw.cz/holmes/
For example, Syria's Web search engine Shamra has its own index according to its founder Shadi Saleh, whom I have interviewed here: https://irsg.bcs.org/informer/2019/07/syrias-first-web-searc...