If you use a search product then someone is going to have your search history and it'll more-than-likely be provided to law enforcement in your country who are the #1 threat to you [0]. It'll also be sent to some sort of data centre for tracking and whatever commercial uses that tracking is good for. I've never understood how that would be a threat, but if you don't like it it comes almost baked in to the business model. You can't stop them sharing data, so they will probably do it for money.

The sell is more that the data MS/DDG has is hopefully going to be siloed away from Google and so it is getting more expensive for an given entity to cross-reference information about you. And if we're lucky competitive pressure will peel DDG away from MS sooner or later if they get larger.

[0] This logic does lead to an argument for a fair chunk of HNs readership to use Yandex, because they are hosted in a country that is effectively at war with the English-speaking world but not presently targeting English speakers.