Does reading Wikipedia offline keep it private?
Largely, yes. Wonder by Zaweba reads Wikipedia from your own PC, has no telemetry and only goes online for downloads you start and update checks.

Reading offline keeps it about as private as reading can be. In Wonder by Zaweba, articles come from an edition stored on your own PC, so opening one sends nothing anywhere. Wonder has no telemetry, and its only network use is the update check and app list, the Kiwix catalogue when you ask to see it, and downloads you start yourself.
Wonder is free software, an offline encyclopedia for Wikipedia and its sister projects. Once an edition is downloaded, reading, wandering and search all happen on your computer.
What stays on your PC
Everything about your reading does. The articles are in the edition file. The reading view shows them, and the page can reach nothing but the local edition, so an article can't quietly fetch something from the internet as you read it.
Your Bookmarks, Read later list and History are kept per edition on your PC. So are the journey map of the last seven days, the subject shelves that grow with the articles you read, and the full-text search index that Wonder builds for each edition. None of it is sent anywhere.
When Wonder does go online
There are three occasions. The update check and app list is one. The Kiwix catalogue is another, and it is only contacted when you press Show what Kiwix offers in the Library. The third is a download you start.
Requests go through a guard in Wonder that accepts only kiwix.org hosts and the mirrors those lists name. Downloads come from Kiwix's servers and mirrors only, and each one is verified against Kiwix's SHA-256 at the end.
How it differs from reading online
When you read any website, your browser asks the site's servers for every page you open. That is simply how the web works. With Wonder, the asking happens once, when you download the edition, and after that your reading is between you and your PC.
That suits plenty of people for ordinary reasons: a student researching a sensitive subject for an essay, someone reading up on a health worry, or anyone who simply prefers their curiosity not to leave a trail. It also suits families who'd rather children read without a web browser open.
A word about shared computers
Private from the internet isn't the same as private from the people you share a PC with. History, Bookmarks and Read later are there to help you find things again, and anyone using the same Windows account and edition can see them. If that matters, give each person their own Windows account.
Kid mode is a separate matter. It switches to Simple English if downloaded, makes text bigger and hides search suggestions and surprise articles containing a list of adult words, and Wonder says plainly that it is not a guaranteed content filter.
The privacy that comes with offline
There is a quiet benefit to having the encyclopedia on your own drive. It works the same on a plane, in a cabin with no signal or on a connection you don't trust. The articles are Wikipedia's own, under CC BY-SA 4.0, each ending with its attribution, and the app around them doesn't watch what you do.
So yes, read away. Wonder by Zaweba keeps your reading on your own computer.