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In my personal opinion, a professional trader is someone who can generate regular profits, and can be repeated, it does not matter how much profit because it can be adjusted in the future, as long as it can be repeated and is sure that it will produce results without breaking the law... I can call him a professional trader...
Then what do you think? Do you have someone who is your reference for learning trading? Or what kind of person is it that you can call that person a professional trader?
Well, you definition is not far different from what I had in mind, I have always seen a professional trader as someone who trades as a profession, this is the simple and straightforward definition.
Trading as a profession simply means that that is what the person does for a living or livelihood, he or she may possibly have other side hustles like owning a business place or have other hand works, but trading is their main source of income and every other thing(s) he is she does for money is simply on or as a side hustle to compliment and support the money they make from trading.
I believe this is a simpler and better understandable explanation than the way you explained yours, though they are still not far different from each other.