Right now, there is sadly no open and private alternative to Google/Bing index. Qwant, DDG and Brave are more like hybrid engines which rely on their own crawler plus a GAFAM index (Bing most of the time). For Qwant last time we knew they relied on Bing for something like 60-70% of web searches. Brave says it’s 95% independent but I don’t really believe them (it’s easy to cheat by including images, videos and news search to increase the numbers). But they do try (mostly Brave and Qwant, I’m not sure DDG really fixes it as an objective) to make their crawler independent. DDG is relying on the GAFAM as I believe their revenue is coming from Bing Ads. Brave Search apparently relies on cryptocurrencies and I’m not a fan of their CEO Brendan Eich. In the end I use Qwant because they seem to try to make their revenue independent by creating their own privacy-respectful ads network (Qwant Ads), even if there have been a lot of issues with them in the past.
As for Open Web Search, it’s good if it succeeds! But there’ve been a lot of people who have tried to do the same before, and I think the result is always pretty much the same: hard to catch up to Google and Bing’s decades of experience in a short amount of time and with little to no fundings.