It seems like a crazy idea to start a search engine competitor in 2023 but the innovation dilemma is always present. We lack innovation, it seems nobody is trying? Do you know of some existing project even at an early stage?
What about the inclusion of LLM based results in Google and Bing search? Regardless of what you might feel about those results, it's certainly an attempt at innovation.
Even if you have the required capital it's hard to get into the market.
Especially as Google also owns the ad market, thus the way to make it profitable.
Only ones I see able to pull that off were Apple, as they have the budget and a platform and with maps were somewhat successful, even though users complained about poor quality initially (I don't have an apple device, thus no personal experience with recent maps), but Google pays them well for not even trying.
Facebook/Meta also stays away from that market and focusses on more "social" platforms.