Firefox

I'm sorry but that is not correct. In the link that you shared to their privacy statement it is explicitly stated that they do not collect your identity when using the service. They say that your identity " is the information we use to ensure that you are who you say you are when you make a de-listing request, report or create an account. This includes: first name, last name, email address."

Furthermore, unlike duckduckgo which to my knowledge relies entirely on Bing's search index, Qwant does actually index the web itself and only uses the Bing index when a search returns insufficient hits from their own index. When they query the microsoft index they send the following data along: "Search keywords; Information about the browser you are using (the User Agent); The first three bytes of your IP address; The approximate geographic area at the origin of the search, at the scale of a region or city; The salty hash generated from your IP address, your User Agent and a salt changing no later than every 3 months; A random token generated by Qwant (aiming to limit data cross-checking)."

I do not know much about DuckDuckGo, but from an initial read the privacy policy is much more vague than Qwant's, not mentioning any specific information that is shared. As they are a US company, they are also not covered by the general data protection regulation.

In general, both search engines seem to do a good job at protecting users' privacy, which to me sounds like something that should be encouraged, not polluted with misinformation.