I agree that "lost users" is misleading if traffic didn't go down, so we've added the word "engagement" to the title above.

As a writer, I know quite much about clickbait name and use them extensively, true that. However, in this particular case, the point is true: ~47% people stopped using the feature (user = someone, who uses). Meaning the conversion between people who found the feature and started using it has dropped by 47% as well.

So, if traffic numbers are EXACTLY the same (as noted) but less people click on a single button, you've "lost those users"? Doesn't make any sense to me. You've lost interaction with a button from your unchanged user base. Like you said yourself, click conversion from your users changed. Users changing interaction ≠ losing users

If you had lost 50% of your users, you would have half of the overall site traffic that you had last time.

Yes and no. I see what you are saying, but in my opinion every site can have its own definition of user and visitor. For some sites the terms may be interchangeable, while for other sites they have completely different meanings.

Let's take HN for example (I don't know if HN considers this their metric or what, just using it as an example.). Let's say they made a change that now requires everyone to login to the site each time they visit. So if you closed your browser window or were inactive for a period of time you would have to log back in. While you could still read posts and comments, you would be unable to submit new stories or comment until you logged in. While you are not logged in you would be considered a visitor. But when you log in, you now become a user.

While at first the traffic, or visitors, may remain the same, without participating users on the site the number of visitors will eventually drop as not as many people are submitting or commenting.

A site that does not require interaction, may on the other hand, simply use the two terms (visitor & user) interchangeably.

Seems to me by losing this argument I'll save 50% users for our feature. I hope you're right and those who stumbled on redesigned feature and left it, will one day return and finally know how to use it.