How does the free version of Cloudflare proxy track users/visitors?

I have embedded a link into the title where a person is frustrated with Cloudflare.

I'm interested in knowing the extent of their telemetry and data collection. The user alleges that Cloudflare collects cookies from visitors when one visits a website using their proxy + CDN?

Just to be transparent: I'm not looking to use Cloudflare, I'm going to use my own setup with a VPS, however it is important to know about such technologies, especially since I work in IT.