Honestly the person who is copy trading is not really after calling themselves anything and just looking to make more money. The point is not to call yourself a trader or not, that doesn't matter at all for them, the point is to get richer and if you do end up richer in the end then you did what you wanted to do and that's it.
I can report from personal experience that people who follow Copy Trader definitely see themselves as (successful) traders. I have a few people in my circle of friends who had tried copy trading at least temporarily and suddenly became "the best traders in the world" ... and also liked to criticize those traders they followed. Of course, this only went well as long as the traders had made profits. With losses one heard - logically - then nothing more of it.
I think that is also in the nature of man. Many simply like to brag about their successes, even if - as in the case of copy trading - they are not even their own successes but simply followed other people.
I think the bigger issue is that they are not making that much money neither, some of them might do it but majority of them do not make a profit and they lose just because they trusted someone else.
I have been following well-known traders like Tone Vays or Brian Beamish very intensively especially in 2017 and 2018. Also these traders usually make the profits with only 1-2% of their trades, so the long term profit and loss statistic at that time was around 48% loss to 52% profits. However, the few percent decide whether you succeed in the long run or not ... It is possible that professional traders participate and let you follow, but you have to follow them for a very long time to be able to take the profit streaks - which will definitely exist.
With short-term follows Copy Trading is more like a gamble - and you will most likely lose a lot of money.