I guess you didn’t get satisfactory answers from your first post, but you still haven’t clarified what you actually mean by your question. All Lemmy servers run Lemmy, so in some senses of the term, they’re all roughly equally private, which is to say not very, because all posts & comments are publicly scrapable, except for private messages.

https://lemmy.ml/:

A community of privacy and FOSS enthusiasts, run by Lemmy’s developers

What is Lemmy.ml

Brother the protocol is called activity pub(lic)

Look for an instance with these qualities:

• Does not use Cloudflare or any other large content delivery network. Instances that use thse allow the CDN to monitor everything your read and write on Lemmy, which can reveal a lot about you even if you haven't used your real name. Cloudflare can then correlate that information with your other browsing habits, and possibly your real identity, because they operate as a middleman for a huge number of popular web sites.
• Maintains a sizable local image cache. Images served from other instances instead of your local one can be abused by remote parties to track what is viewed on Lemmy with your IP address (and sometimes your browser signature). Alternatively, you could block off-site images using a browser extension, but that would mean not getting to see as many pictures.

Lemmy.today is a very neutral instance