It's perhaps a bit on the side but still part of the topic of search.
Have you noticed how newspapers systematically do not supply a clear source for their articles? It's especially prevalent on political cases where there are easy-to-link paper trails. This makes it a lot harder to find the source for their article, so you end up just taking their word for their angle on the story.
A great recent example is Biden's Executive Order on the protection of women. When the newspapers writes about his EO, they're never doing it form a neutral standpoint. In this case they're either pro or anti abortion. But if you want to know the contents of Biden's EO for yourself, then you're forced to search for it. And depending on the search engine, that might also be hard because also search engines are politically biased.
Just so we're clear, this post isn't pro or anti abortion. Instead it's an example on how newspapers systematically force you to take their word for their angle on any given news story. So if you want to know source material, then you're forced to search for it. And when you do search for it, you're then at the mercy of the political bias of the search engine.
For that reason I'm not so sure a non-profit search engine will make political biases go away, especially when you consider what happened to Wikipedia. While not a search engine, it is a non-profit and communal project that set out with the ideal of being truly neutral, but in the end it failed at that, and some would say spectacularly. And the main reason is exactly bullshit, or rather the BS that comes with political bias.
Don't get me wrong, it's still a great source for information, but when you search for any topic that is in any shape or form politically sensitive, then you have to know about Wikipedia's clear political bias beforehand, or else you might take their angle as gospel.
This is especially insidious when it comes to search engines and also social networks, because most people assume that what is shown to them there is neutral, or at least coming from a friendly party. But then it turns out, that's not always the case.
When you systematically get biased information, then it's a democratic problem, because it prevents people from making up their own mind about political topics. Thus when people finally vote, the risk is that we get a society that does not reflect peoples actual opinions.
I think most people in here has been on the receiving end of that, no matter which side of the aisle you're on. And the result is always resentment and bitterness which in turn does not make for a healthy democratic environment.
Instead the political bias should be more clearly visible and out in the open on both newspapers, encyclopaedias and search engines alike. And while a non-profit search engine would certainly save you from corporate interests, it still won't save you from political ones, though it might be a good trade-off to save privacy.