Afaik, Zen adds no privacy features of its own. What they do do is include the Betterfox template ootb (which is a Firefox settings template like Arkenfox with some differences, and not solely privacy/security related).
I’d estimate, it probably falls somewhere between Firefox configured per PG’s recommendations, and Arkenfox, but most likely more fingerprintable due to the UI/UX changes and being a niche browser with a small userbase, and some rather unique UI compared to other Firefox forks.
Then there is the trust factor to consider, you are adding another party to trust (trust to not be malicious, trust to be competent, trust to make sound security/privacy choices and update in a timely manner).
The nice thing about Firefox forks is they are all pretty similar. Most don’t add much of their own under the hood, so if you understand the building blocks they use (e.g.Zen and Betterfox, or Librewolf loosely basing off of Arkenfox), its pretty easy to get a rough idea of the level of privacy they offer.
The TL;DR of my perspective is: Zen Browser isn’t especialyl exciting for its privacy attributes, it doesn’t contribute anything unique, but it isn’t unattractive either, so if you are attracted to Zen for other (non-privacy) features, then it seems like a reasonable option, for a reasonably private browser with a UX that appeals to you more.