At first glance, a "private" page does not directly process personal data and would therefore not require a privacy policy.
So if you don't use contact forms, advertising banners, social media plugins, etc., you should be on the safe side.
What most don't see: The server on which pages are located (hosted) collects personal data in the background in the form of server log files. These log files contain IP addresses, these addresses are personal data.
So yes. Even if the server doesn't log the IP to logfiles as it still receives the IP every site needs a privacy page.
There are good privacy page generators, though. Free of cost.
Well, I'm not in Germany... you didn't mention in your original comment that it only applies to German websites!
Everybody else. Officially if you target European audiences you would need to adhere to the same regulations, but practically nobody could reasonably enforce it.
Really? I have a small personal website with no tracking; I guess my hosting provider collects server logs, but do I really need a privacy page for that?
An imprint is something I've only seen on German websites (I recall reading somewhere that those are required by law there).