Personally, I would e.g. support a search engine as a public service funded through EU budget, but I’m in a tiny minority with that opinion.

I would get behind that, rather than pay some private company I do not trust. At least something EU-controlled, would be a bit more trusthworthy, than some shady business from who knows where and under what actual ownership. I do not trust company privacy policies at all anymore, all of them are lying as much as they can, since there are no real repercussions for it, except losing paying customers - which they will not lose, since they are able to lie as much as they want.