score:3
After a while I noticed that it is possible, so I post the answer that might be useful for someone. First, I completed myProfile details which I haven't done so far, I added phone number, nationality, date of birth. After that, it showed me my currently added travel document that I have got saved on myRyanair account which was my passport. But there also appears an option Add another document. So you need to click this and add the details of your ID card and save. From now on, when you click on Check-in button for your flight reservation a new document should appear in the scroll down menu and you can select it. Thankfully, I didn't have to pay anywhere :-)