Sincere question from someone who doesn't understand why we're freaking out: Why is this different to you than a password manager doing the exact same thing with password fields?
Here's what I see: someone installed the DuckDuckGo extension, which now has a new feature. That feature is best implemented by having a little widget that allows creating a new alias. Users who haven't seen the widget before wouldn't know how to use it, so DuckDuckGo added an explanation for people who click on it without having set it up yet.
Where was the line crossed? Do you object to having a widget at all? Is the problem having an inline explanation introducing the feature? Is it the phrasing of the pop-up?
I see a lot of visceral reactions and condemnations, but I don't see anyone explaining what makes this an ad and not onboarding.