It would be much harder to know what exists beyond "GBY" (Google, Bing, Yandex) and how it all works without the work of Rohan “Seirdy” Kumar. For three years, Kumar has been updating a heavily annotated list of search engines with their own indexes. It is 7,000 words, but only a portion of it deals with engines offering general indexing, in the English language. You can read Kumar's evaluation methodology for a better understanding of how he compared and assessed sites.
What stands out? Mojeek ("it's not bad… I'd live") and Stract ("a useful supplement to more major engines") are two of Kumar's favorites. Right Dao has "very fast, good results," in part because its crawler starts off from Wikipedia. Yep reaches farther out, showing results that link to and back from sites related to your query and also promises to share ad revenue with creators. All of them show promise, but you get the sense that they're a second car, or a third bicycle, rather than a primary transport.
There are far smaller-scoped engines in other sections of Kumar's post. If you're wondering where that one other search engine you've heard about is, it's probably in the "Semi-independent indexes" section, because it uses a GBY index when its own results are not strong enough. Here, you'll find cryptocurrency-friendly, controversy-courting-founder-having Brave, a few engines that either "resell" GBY results or stuff affiliate links into them, and "the most interesting entry," according to Kumar, Kagi.
Kagi requires an account and uses its own index, Teclis, in combination with Google, Bing, Yandex, Mojeek, and others, including, notably, Brave. Kagi's founder has strong opinions on the AI-based future of search and responding to harmful searches in ways that are not "scalable." How much of that does or does not bother you will vary, but it's worth noting that Kagi also suffers when the GBY triumvirate is restricted.