i don't have anything useful to add except that I'm saving this because i also want to know the same thing as you.
hoping to learn how and start hosting my own matrix server over summer. depending on how things work I'd like to migrate my family chat there, possibly even host space for my kid's friends if that's a thing they have interest in using
eventually we'll all be able to have an open source AI that runs fine on a phone or any average device and we'll have our privacy, and the big corps will lose their grip and hopefully collapse
there are plugins that allow you to write your own CSS for a website. if you know enough CSS , and depending on the structure of the search results, you can probably make a style rule to hide things based on the domain
i think the difference was only ever going to be when they felt like running the extra processing to do the work.