I self host just about every service I can, including search.
You're asking for a guarantee, which I've repeatedly admitted I can't offer because absolutely no one can provide that. No provider, no service, no software. All we can do is decide what we each consider to be actions/behaviours indicative of trust and use their offering in a way that maximises privacy for us as individuals. I put more trust in software/services that has code that anyone can read, that has been independently audited, that is trusted by the community and possibly tested in a legal environment. You might put more trust in things like privacy policies and other legally binding documents. Neither of us can guarantee anything however. I've lost count of the number of companies who've violated privacy laws and users only find out years or even decades after the fact.
But I'll say it again - whats right for me might not be right for you and that's fine.