I’d use Kagi, but anonymous searching is impossible because you need an accoint to use the search, due to it being a paid service. I just have to take their word that they maintain privacy. I don’t trust any company’s word for shit. Also AFAIK it’s not open source, so I can’t self host it either.
Also, it’s quite expensive when other options are free. I get why they do it this way, but it’s just not for me.