They are definitely not free! (I don't know how does it work in Dragon Age, sorry :'D ) They are owned by the King or Queen of the kingdom they are born into. The royals provide them with education so they can control their magic and don't accidentally become monsters. If they are powerful enough, they can be court mages and get gifted honorary titles like Lord and Lady, but no land or servants. If a witch is not that powerful, they can become village witch, but they are still belong to their kings, and have to follow all their orders (kinda Howl's moving castle style)
Jon case is special in a way that he became a witch from a really young age, when he was 8. I kinda follow 'the first mark of a Fear of canon = first sign of magical abilities in this AU' logic. So for example, Mike Crew was also a witch from childhood, but Lady Jane Prentiss only started dubbeling with magic when she was an adult.
Jon doesn't want to be a court mage, but at the same time, he wants to be a witch powerful enough to stand up against Elias one day. Nobody knows this, just that he is refused the title of being a Lord. He also knows that Elias can see his every move, and he is afraid to tell anyone about what happened, fearing Elias would would take revenge on them.
Thanks for the lovely ask, I also made a comic inspired this, of how Jon would talk about his situation :3