This is exactly the reason I've been considering if it's possibly the time to start and launch a brand new search engine, especially now subscription based systems are so common.
With at the core a pledge to not record and/or share any user data or interaction and supported by a subscription service for who wants to pay and really oldschool tier selfhosted "sidebar" ads for the rest.
None of this "insert ads into content" shite.
For the algo, also far more oldschool "less intelligent", where keywords and content matter (backed by a curation of good/bad sites) and options for users to report sites, that will then be re-curated.
For adding sites, allow subscribers to suggest sites that then get listed to other subscribers (or if it grows large enough to support employees, subscribers AND employees) for validation.
If a site is then later found to be questionable, everyone that suggested and validated it can get a negative validation score, which will be used for future reference when selecting users to validate new sites.
Something like they get +1 for every validation they do.
But -1 for 1 bad validation, -11 for 2, -31 for 3, -61 for 4, -101 for 5, etc, so if they validate 100 sites and validate 5 incorrectly, they are no longer allowed to validate new sites.
And for validation, once there are enough subscribers, you take 100+ random subscribers, of which 50% needs to respond to validate and if 90% of responders validate positively, it passes. If less than 90% validate positively, it goes for manual review by the administration.
Etc etc.