To put it simply, they "cast" but these people aren't limited to like a certain affinity for an element. They aren't locked behind something like that but I also don't want them to be also "too OP" right away in a sense. To think with ideas and emotions mixed together and that they can will it to... well make it happen.
Here's my two cents (the idea I offer is for a darkish story, I got carried away here and wrote a basic plot for a novel lol. But that's how I would think when writing a fantasy story: set environment => derive the rest of environment
=> add characters and how they would act in this environment ) :
What makes magic, magic? Well, to me, magic is something
supernatural, something
beyond whatever reason, logic and laws of nature should allow.
Since you want to use "ideas and emotions", how about using the word "will" as an umbrella term for them? And since you want to use will as a component of magic, then perception would be a key component in it.
Then, I'd use a lot of symbolic imagery for spells. Here's an example: some sorcerer cursed a mirror and ground it to dust. After scattering the glass shards all over an area, somebody got this dust in their
eye, causing them to
think differently from before. Here I used the symbolic connection between sight and perception and between perception and thinking (or will).
Another example: raven got cursed with
blood of a victim. The victim ended up having a long life but their heart grew dark.
Here I used the connection between blood and its symbolic meaning of tying people together (blood ties) as well as the heart's connection to blood and heart's symbolic meaning of behavior, belief and love. Ravens are associated with longevity and their black appearance is used with the meaning of uncleanness.
I think this makes for an original enough magic system that can be either extended to a very hard one or be used as a soft system.
But first, you want to put limitations on your magic system.
Let's first go to the source of power. I would use demons/other entities as the sourse, because that would allow me to expand the lore, but you can do whatever, tbh.
Let's say that by using magic, the caster "opens" a door in their heart(will) to the other side, also referencing vampire lore, where they couldn't enter without an invitation, but extending it to all supernatural entities. Them entering, obviously, being metaphorical.
So, the longer someone uses magic, the more susceptible they become to the influence from the other side and, physically and mentally, they become more
worn out, losing the original "non-fantasy" characteristics (like, turning into zombies, ghouls, vampires etc) and their ability to interact with the not-magic world also becomes smaller and smaller, as they get pulled to the other side. Let's say their will also gets eroded as they pay with it(their souls) to the entities providing magical powers.
So, we came to the first limitation:
1) magical things become more expensive the more it comes with contact with the "real" world. Especially "real" people.
The last bit was added because the entities need payment in form of the will of "real" people, so if the "real" people could interact with the entities casually, it would take away from the idea of separation of non-real, fantasy, things from "real", not fantasy.
Then, comes second limitation
2) mages should either do magic secretly, or pay a lot.
Which could add an additional limitation
2.5) mages don't teach their knowledge casually, as it also requires affecting the will of others, therefore, a price
Also, there can be a third limitation
3)the more a person is susceptible to believing in magic, the easier they are affected and theess a person is susceptible, the more they are affected
Therefore
4)mages tend to cast spells that can be reasoned out to be non-magical, as the price is not as steep when doing so
And
3.5)mages tend to operate in places away from civilization, as they have more power there. Especially in places with no people.
4.5)mages are often well-versed in sciences, because it would allow them to come up with explanations for their spells. They are also good with rhetoric.
Also, a battle of mages can be made interesting if
5) mages can also fight by making their opponents lose believe in themselves, lose concentration or some other way in the same vein.
And how about another limitation
6) if a mage doesn't want to waste away too quickly, they have to take breaks from magic to recover their sanity.
Of course, not every mage will be fine with their fate, so they want to change the real world to beore favourable to them. Let's say there are factions:
1) extreme anti-civilization faction wants to bring back the dark ages
2) mild anti-civilization wants to make the role of science less important, make people believe that it can't solve a multitude of problems so that peoe believe in magic more
3) mild pro-civilization faction wants better growth of technology so that people can buy that a lot of magic is just technology
4) extreme pro-civilization faction, aka mage hunters, just hate magic and are afraid that the other side will grow powerful enough to affect the real world directly so they want to kill all magic heritage
Now, let's describe the process of payment:
Usage of spells should have a direct and immediately visible effect on the caster (because otherwise it would feel like some deus-ex-machina)
Things like, loss of mood, loss of appetite, headaches, visible ageing, hallucinations, whatever else to show that the caster is losing grip on reality.
A mage would often muter to themselves, cackle creepily or get weirdly focused on something, disregarding everything else.
A numerical representation would be fine, but it's not necessary.
So, this way the magic system would not be op and not limited to affinities or attributes. It's also pretty original
That along the way also makes me really try to think of how do I want to develop my MC since they're... well the protagonist. Aside from character development, I hope to try approaching the hard way first so that it will seem that the MC has difficulties first.
This also means that it matters with their life because it's a part of them now, a chance to become something else too
This can be done quite simply. Mc has some rl problem: let's say their relative or themselves have some incurable fatal disease. Mc finds out about magic. Mages don't share easily and ways of borrowing power from entities are all about information : what rituals to do and how and when to do so, how to bargain for a good price, what never to do etc.
Mc tries finding knowledge in that circle and it endangers them as they are now "open" to the influence of magic and have no means of protecting themselves. They are attacked by ghosts and monsters and they end up getting into all kinds of accidents
After mc acquires power, they may use it to escape from their troubles, because the nature of magic makes mages tend to lose grip on reality and contact with normal people and now they have to balance their real life and the troubles that having contact with the other side entails. They lose grip on themselves, so they rely on their family and friends not to lose their identity, which causes their concern.
Mc can't get other people into "the game", as 1) they can't afford it and 2) they don't want their loved ones to face the consequences of being in "the game"
Mc can't pull out, it's too late for them. Now they have to either try to live with an additional burden and slowly solve their problem (as they can't magic the terminal illness away immediately, they don't have that much power and can't pay) or they can live in a perfect world of their dreams while indulging in magic(alone, a mage can do pretty much anything as long as they pay the price, so things like a very long life and youth, comfort, they can hang out with lesser magical creatures(not entities that grant magic, but beings that can do magic on their own, but can't affect the "real" world) like dryads and elves and mermaids) , but they would have to lose their normal life and eventually, themselves too.
Then they can mature as individuals and learn how to cherish what they have and use their maturity to bargain with the other side better. They can use small magics to help them get better in rl (buying health, beauty, wealth) and get better at sciences to become a better mage.
They attract attention of the factions
The factions have table manners for acting in "real" world, as any mage can climb to the top of it with relative ease
Also, say, the entities behind mages are having some conflict, so the prices against mages under conflicting entities drop and dead mages under an enemy of your deity yield rewards. So, mc, a young mage gets swept up in this and rises through the ranks