Making Magic Magical

I love magic. In video games, I try to focus on characters who can use magic as much as possible. Any story that has magic immediately draws my attention over others. It's sparkly, it's colorful and it'sAsexuality FAQ a powerful literary tool. You can be truly creative about your setting, create unique situations that challenges the audience, and explore different facets of human psyche and society. Unfortunately stories that have magic often don' put the necessary thinking into it and they end up becoming mundane.
Now, let's look at different approaches to magic and their strengths and weaknesses giving magic a magical touch:

Magic as a Mystical, Unknown Force

Mystical magic is ironically often the most relatable to us because throughout the history people who believed in magic or supernatural forces often thought it was something mostly beyond human understanding and while it is not very popular today, in classic stories magic was depicted as vaguely as possible.
It is widely thought that J.R.R Tolkien's works, Lord of the Rings and Silmarillion, originated every medieval fantasy cliché ever but one way Middle Earth is quite different in most fantasy settings and much closer to fairy tales and legends is that magic is incredibly vague, doesn't really exist outside of divine forces, and it is rarely even mentioned as magic most of the time.
Magic in A Song of Ice and Fire is also quite similar. This is a case where I think that distinction of low fantasy and high fantasy isn't quite useful. People often think series as a civil war simulator but looking closely, it becomes clear magic is highly important in the setting - ironically more important than some settings where magic is functional - but as an unknown, grand, eery force.
The benefit of this approach is it lifts much of the responsibility from the writer. You are truly free to make it impactful or low-key as you wish. When magic is depicted as mystical it is often employed as metaphors and symbolism for this reason, like the One  Ring in LOTR or dragons in ASIOAF. Obviously it works very well for horror stories and abstract works where the things not making sense is the primary narrative function that magic provides.
The weakness of this approach is you might end up putting too much pressure into the audience's suspension of disbelief, especially if you also want to make magic very visible in your setting. And people usually aren't very keen on seeing authors referring to magic to solve plot points constantly.

Magic as Knowledge, Technology, Science

Imagine a typical magic school setting. You have a clear route how to do a certain magic. You input x, it outputs y. You study how to do it. Sometimes you need an inherent talent, sometimes you don't. You can use wands, runes, scrolls, some kind of sacrifice, your voice, your hands or just with your thoughts.
Sometimes you don't even study, magic is readily available as gadgets for everyone, making it more parallel to real life tech, such as Orbal Gears in Trails in the Sky.
What you can you do with this magic? You can throw fire, water, ice, lightning at people, summon storms, rains and meteors, make things explode, fry things with sun, petrify things, create earthquakes, throw lava at people, blast them, make people ill, make people heal, make people sleep, wake people up, summon skeletons, golems,  demons, make corpses walk, stop time, go back in time, change the size of things, turn things into other things, teleport, carry things,fly, be invisible, change people's thoughts and feelings, read people's mind, curse, bless, command plants and animals, disintegrate things, shoot people with pretty magic rays, create magical items to do all of these...
Now think about this: Can you suspend your disbelief for most of these in a sci-fi setting too? Your answer is likely yes. We can do most of these in a real world setting too, even without requiring too much effort. Like I said before: input-output. Magic is no different from machine or even more aptly, a computer program. You can get your power from divine, you can be chosen as a magical girl, you can draw it from a magical tree, you might have limited uses before you need to memorize again, but behind all the spectacle it's just engineering and science for a mostly medieval-ish setting.
This style is incredibly popular in fantasy works and it's not hard to see why. It's much easier for readers to buy, it's easier for the authors to explain and for games, input-output system can easily be turned into gameplay. The popularity of functional magic and shared collective memory of fantasy works makes it even more standardized and familiar. But this creates two new challenge for authors:

• How do you avoid being too familiar? Perhaps magic should feel a little more "magical". I might be a huge nerd to care about this much but if your fire magic is perfectly indistinguishable from a flamethrower, why your setting just doesn't have a flamethrower instead, heck, Star Wars shows that you can perfectly have sword fights in a highly advanced setting too. Why do you really need magic?
• If your magic is functional, you can't just make it appear and vanish at your demand, it's alive and it will impact the societies in your setting. It will raise ethical and sociopolitical questions: Who magic really serves to? If magic is hereditary what stops wizards from taking power? Why standard medieval battles are a still thing if you can just burn someone's face in an instant? What functions potion serves that regular magic fails? Honestly, this is a very large topic in itself.

How do you overcome these challenges? There are different approaches.

• You fully embrace functional magic and make it actually indistinguishable from technology like Trails in the Sky and explore its consequences fully.
• You can have a setting both technology and magic exists, separately. This allows you get more mystical about magic. Of course this brings it's set of questions but I see that it can work.
• Or you can pull a Harry Potter and stop exploring your setting mid-way to focus on your teen drama. Consider this: You can turn objects into other objects. When the money issue brought up, it is said that you can't turn stuff into money, not because it is banned, but because it is effectively blocked. Can you think about the implications? Someone or some people have the ability to just limit other people's magic! It's clear like day and night that Rowling never thought basic questions like "Why printing money is such a big deal, why they can remove outright harmful magic too?", "Who decides what gets to removed?", "How people can limit magic, is there a source of 'anti-magic' in HP universe?" It would be nice if the writer thought about implications of magic in setting instead of just adding them like theme park attractions, just saying.
• I don't recommend pulling an Elder Scrolls either. The lore sure promises you all the cool and otherworldly stuff you can do but what you really get is all the bog standard magic kit, which got even more boring as the series went on. Magic can achieve so much in that universe but despite being constantly praised as prophets and god-slayers the best we can do is just sending a somewhat. large ball of lightning
• What I do recommend is, if you want to make magic central in your setting make your battles turn-based or at least pausable. It's not a coincidence that, all video games that has magic that come close to being interesting use such battle systems, turn based battling really allows you to put truly out there stuff. There is not much difference to player between commanding player's hand to throw a magic ball and commanding player character to throw a magic ball either, most of the fun about magic comes from watching its effects, so a turn based system might just be perfect.
• One approach I see that consistently work is Magic as creation or forces of nature. It's something that audience can easily understand, it makes boundaries of magic limitless, it allows you to be functional as much as you want while protecting its mysthical nature, opens you up to shape your setting as you like A good example of this approach is Earthsea series. Magic is both a grand force and a central part of the universe while being functional and affects the everyday life at the same time.

As My Mana Runs Out

What do we get from all this? Magic is an indeed powerful tool. It can truly make your setting shine or highlight how uninspired it is. Like a magician carefully chanting words or an alchemist meticulously prepare potions, a writer too must be deeply considerate about their writing. I mean sure, you can still have popular series that makes a lot of money. But nerds like me won't like it, and will write overly long articles whining about it, you wouldn't want that! But, seriously, it will probably more fun to you if you add a little more sparkles to your magic too...