So for the uninitiated in this thread: in fantasy, 'hard' refers to fantastical elements with hard, defined, clear rules. Dungeons and Dragons has a pretty hard magic system (All video games that use magic have hard magic systems by definition), so does Avatar: The Last Airbender, and most novels written by Brandon Sanderson (which are amazing if you haven't read them.) Other things like the Nen system from Hunter x Hunter and Chakra from Naruto are fairly hard magic systems. you use the magical superpowers to do a thing, you do it intentionally, you know what the capabilities of different kinds of magic are, and they operate on rules and logic that may not be strictly realistic, but can be clearly understood.
A soft magic system refers to one where magic is weird, esoteric, beyond human understanding, and not necessarily logical or consistent. Lord of the Rings has very soft magic in it as a good example. Other soft magic systems include Chainsaw Man's demon contracts, Jojo's completely flexible and indeterminate limits on what stands can be or do, and Harry Potter's inexhaustible list of spells that can do... whatever the hell you want them to, apparently.
Of course, this exists on a spectrum: Lord of the Rings has an extremely soft magic system, while Allomancy from Sanderson's Mistborn books is an equally hard magic system, but it can be anywhere inbetween.
Harry Potter is a somewhat harder magic system, since each individual spell has a specific function and potions have to be brewed according to specific rules and recipes. I'd still argue it leans softer because there are new spells introduced every five minutes and seemingly no rules on what can or can't be done by any given spell, so you just have a bottomless list of things the magic can do whenever it needs to.
Meanwhile something like bending in Avatar is a mostly hard magic system that leans slightly soft due to the very spiritual nature of accessing the magic. What bending can or can't do is pretty clearly defined, but the exact details of the ways it can affect things, especially when spirits get involved, can be a little fuzzy depending on what's needed for the story.
I've referenced Brandon Sanderson a few times in this, and I 100% recommend checking out his stuff, as well as some of the creative writing lectures he's done (free on youtube), and he has outlined three 'laws' of magic that he uses for his writing:
1: The author's ability to resolve conflicts in a satisfying way with magic is directly proportional to how the reader understands said magic.
If you want your characters to solve problems with the magic system, then it needs to be a hard magic system that the reader can understand and follow. Soft magic can get characters into problems, but only hard magic can get characters out of problems.
Good example of this: How many times in Lord of the Rings does Gandalf's magic actually save the day or fix the problem? Since the audience has no idea what spells and abilities Gandalf actually has, it would be unsatisfying for him to just pull out a spell that could poof away whatever issue the characters are facing. Magical shit gets the characters into trouble all the time in LotR, but magic, at least by itself, rarely if ever solves the issues.
2: Weaknesses are more interesting than powers.
What your magic CAN'T do is more interesting than what it CAN, and this is where you make your magic systems interesting and creative. The World in Jojo's can't stop time for longer than 5 seconds, so what can the character using this stand do in 5 seconds to give themselves an advantage? Jutsus in Naruto can't just be made stronger by pumping more raw power into them, so what do the characters have to do instead to make their abilities stronger?
How your characters work around the limits of what magic is capable of is going to be more interesting than what the magic is actually capable of to begin with.
3: Expand, Don’t Add.
More powers are not always better. Luffy from One Piece is a perfect example of this. He is made of Rubber. That's his whole thing. That is all he's got for nearly the entire series. Instead of getting new things he can do outright, he finds new ways to use that single ability in conjunction with other stuff. Force his body to pump blood faster in order to increase his speed and reaction time, store energy by stretching his rubber body and releasing it in rapid bursts, reflect bullets by blowing himself up like a balloon and catching them.
Luffy took 500 chapters to test and experiment and find the limitations of ONE superpower, never actually gaining new abilities but finding new and creative ways he could use his rubber body. Then he got one additional superpower in the form of Haki, and spent another 300 chapters JUST exploring the ways he could combine this single new superpower with his old one before getting anything else.
I think if you want to find a way to soften your magic systems, then just think about your magic more like a neutral force of nature. It exists outside of your characters' control, at least your central characters, and it might be used to their advantage or to work against them, but never with intent on the part of your characters. Magic is beyond them, whatever rules or limits it has are not logical or sensible to a regular human brain.
The works of Hayao Miyazaki tend to be pretty good at this. Spirited Away comes to mind, with a fantastical world and tons of magical shit happening at and around Chihiro, but basically none of it is under her control. When she does magical stuff, it's solely at other people's explicit instructions because she has no damn clue how any of this works. When Chihiro overcomes magical obstacles, it's not through using magic herself, it's through honesty, determination, and resourcefulness. Magic gets her into problems, but she gets herself out of them.
Generally speaking, all the same shit applies to Sci-fi as well: Hard sci-fi is stuff based on real, actual science, soft sci-fi doesn't give a shit about the laws of physics. Something like The Martian or The Expanse are great examples of harder sci-fi, while Futurama, Rick and Morty, and Star Wars are just about as soft as Sci-fi can possibly get.
There's other principles and ideas to apply to the genre that aren't quite applicable to fantasy, but the gist is generally the same. Only have alien physiology be the key to solving an issue if the audience actually understands that alien physiology. If it suddenly turns out that the Glaknoo people have a special Blarflag Gland which makes them immune to plasma rifles that is only revealed immediately after being shot with a plasma rifle, that's about the same as the wizard casting 'nuh-uh no you didn't' because you never actually defined what the magic system is capable of.
The harder the sci-fi or the magic system, the more effectively you can use it for a combat system, for duels like a shounen battle series, or for outright problem solving. The softer the system, the more your story will need to focus on character conflict and relationships, using the sci-fi or fantasy elements as a backdrop and atmosphere more than as a direct agent in the narrative's resolution.