One thing you need to think about is the character's immediate reaction on discovering they have powers.
Since (like most people, I think) I sometimes have dreams that I can fly or do other impossible things, I would wonder if I was dreaming and try to wake up. When I am dreaming and try to wake up, it usually works. Since it wouldn't work in the case that it is true, I might need more convincing. Am I sick? Did I absent-mindedly take too much of one of my medications and am therefore hallucinating? And so forth.
It wouldn't really be difficult for me to believe in magic, but it would have to be the kind of magic that people who really HAVE believed in magic have believed in, magic that requires knowledge and effort, not the cheap, easy kind of magic you see in games and quite a number of fantasy novels. Since the kind of magic you are talking about is that kind of magic, I would not be easily convinced.
But once I was convinced, I would probably want to test it. Your idea to make action figures fight each other sounds like a reasonable test. But you know, just about anyone can make action figures fight each other even without magic. All it takes is two hands and a voice. To do it with little more than a thought would have a certain novelty factor at first, but it wouldn't really impact my quality of life, so I think I would soon grow bored. (To make the statues and statuettes of dragons and other mythical creatures I have around the house and garden move and talk appeals more to my imagination and I think would bring me more pleasure, but even that would be something I'd only want to do occasionally, as I wouldn't want to spoil it by making it too commonplace.)
Once I had convinced myself and experimented, I would definitely want to be discreet in how I used those powers. History tells us that other people don't deal kindly with those they believe have magical powers. Also, I can see how people with other kinds of power (politicians, crime bosses, etc.) would want to use me for their personal ends. In the case of criminals, if I refused they might try to convince me by hurting or threatening my loved ones. There might be other reasons to keep my powers secret, but these are the ones I thought of at once. I'd have to be amazingly powerful to keep myself safe from a large group of people trying to do me harm, and I would have to spend a lot of time being vigilant to keep those I care for safe . . . so, yes, my best choice would be to keep my powers secret.
I'm not drawn to this idea. Who am I to think I can teach these people a lesson? Could I even teach them a lesson, really? It sounds good to humble bullies and make them feel small, but many people who are bullies already feel small and it is by bullying that they feel big and powerful, so "humbling" them might make them act even worse. Unless my powers included mind-reading so that I could tell the difference between these people and those who do the same sort of things because they are selfish and cruel, the malignant narcissists. But by using my powers against those I judge deserving of such treatment . . . well, it's a slippery slope, and I can see it bringing out tendencies to malignant narcissism in myself, so better not to do it.
I would be much more interested in trying to provide secret help to people in need. Although even there, there is a danger of unintended consequences, so I would want to be careful and think things through . . . except in cases where the need is immediate and urgent and I am right there at the time.
It might well occur to me that if I have such powers, other people might have them too. If they have had their powers for quite a while they would be more experienced and therefore (I hope) more wise in how they use them (having learned from any mistakes) so I would try to find them in the hope that they could provide valuable advice. And maybe we would work together. Especially if there was a group of them. Yes, that would appeal, to be part of a secret society with the power and experience to make a positive difference. But then I would consider there are probably bad people with the power, so I'd have to be careful who I trusted.
Really, it doesn't sound like a lot of fun. There would be satisfaction in helping people and yes wielding the powers could be an amazing experience with the potential for mind-blowing moments of wonder and adventure, but on the whole it sounds like a huge responsibility and one full of moral dilemmas, and so many dangers to myself and my family. Until I came to terms with all that, I suspect I would have moments of sheer terror just thinking about the possibilities for things going wrong.
A most fascinating and well thought out answer. Thank you! You’ve given me much food for thought as I progress in my journey of writing out this idea. I’m inclined to agree that meddling in politics would not be a good idea without being adamantly sure that you wouldn’t get caught, which is to say it’s better to avoid it. I was thinking possibly a defunct secret society, possibly men of letters -esque, that left behind potential references for my “guy(s) in the chair(s)” to use. The first story is going to be about revenge though. Not against a human, in case that caused concern.