So for someone amateur or advanced player. Is it recommended to also do it this way or let it 'free'?
Hm i wouldnt give any advice for that, because that highly depends on your abilities, technique, overall playingstyle, your physique... so many factors.
But i got curious and wondered what i am doing with my free arm. I guess i would let it fly pretty far away from me but actually, the only thing i sometimes use, is my upper arm. That is moving away from me from time to time to hit harder fh topspins. My forearm however remains still and is pointing forward to the table most of the time.
The main movement should come from your legs, into the hips, rotating through your core into the chest>shoulders and whipping with your arm. That movement would be ideal and is faster if you dont need your free arm for it. But if your core, legs or smth else might be lacking in power, your body will find a substitution for it.
So to somewhat answer the question i would work on leaving the arm tucked or just slightly free. But if that feels awkward or unnatural for you, i wouldnt change that forcefully.