Offramp has no server of its own and sends no analytics.
Two actions make it contact status.d420.de, the public tracker that health-checks Nitter instances. One is your press of the Check button. The other is opening an x.com link while the stored reading is more than 15 minutes old; this second case is on by default, and the settings page turns it off. The tracker's operator sees your IP address and the time of the request. That timing reveals that your browser opened x.com, so the manifest declares the collection of browsing activity, and Firefox shows you that declaration before you install. The request itself is a bare GET. It names no page, and no cookie travels with it.
A press of Check also fetches the front page of any mirror you added yourself that the tracker does not know, because asking directly is the only way to learn whether your own mirror answers.
Redirected navigation goes to the mirrors on your own list. You chose those hosts.
The statistics stay on this machine, and no counter holds an identifier. Counting which accounts you read is off by default and capped at 40 handles. Switching it off erases the handles it gathered. A private window is redirected like any other window, and nothing it does is counted. The Reset button erases everything.