There is definitely a probability to deal with a non reliable instance admin, but not less than with any other social media, and in principle they collect even less data

Yeah. You can see the cookies that are stored by a site by right-clicking on the site, going to "inspect", and the clicking "Storage". By default, the only cookie that Lemmy has is an jwt cookie used to authenticate your user.

You are not asked for a phone number to be here. Providing an e-mail is often optional and even discouraged by some instances. When you want to send a private message through the site you get a message discouraging from doing that and encouraging to try to use an encrypted chat application instead, such as matrix.

The original Lemmy instance (lemmy.ml) is a community for FOSS and Privacy enthusiasts. What is asks from a user and what it does with the data is what it needs to be functional. Lemmy lets you take any proactive step that you would like to take to protect your privacy - use a VPN or Tor, use safe passwords, use a unique identity, and don't provide any personal information. There are no built-in features to block you or discourage you from doing that. Lemmy never asks for your location, nor does it keep any logs of what content you visit, nor does it try to run any analytics on you. But even if that is not enough for you, the fediverse doesn't lock you out, you can set up an instance or even create a new program to interact and communicate only precisely what you want to communicate via activity pub.