If Google pulled out, Bing would lowball Mozilla. Yandex are untouchable given that they're Russian and so there's not much left.
But that's all besides the point, removing one dependency to replace it with another doesn't make sense, people have been clamouring for Mozilla to become self sustainable and they're attempting to do that. The fact that people want some crazy utopia where Mozilla just replace Google's money with donations is the problem. Though, I personally think that we as users, should be lobbying our governments and advocating for more investment in open source alternatives such as Mozilla.
Mozilla was surprisingly close to having its own search engine, if you count its partnership with Ghostery several years back. But Brave, a company with presumably fewer resources, bought it out.
If anyone else offered to pay what Google pays Mozilla would drop Google like an hot potato (like they did Yahoo).
So I wouldn't count on any mythical alternative unless Microsoft decides to waste more money promoting Bing (which wouldn't really be an upgrade privacy wise).