The spell slot system as implemented in 5e was first seen in a video game called Wizardry; they called it “spell points” in that game but you had separate pools of “level 1 spell points”, “level 2 spell points” and so on, just like 5e’s slots.
So for a more JRPG-like vibe, you could lean into that. Call slots spell points or mana points or magic points or whatever game you’re more familiar with—not only video games, there are other table top games that uses MP. The hack, compared the cockamamie spell point system option in the DMG, is to just keep “the separate pools per level”, just like slots work now—i.e. don’t change anything, it’s just a new name for them.
One thing that could be fun for some settings would be to rename slots
“mana”, and every time you level up and gained more mana, you needed
to select specific places associated with the mana. For example, you
go from level one to level two, so you gain a third level one slot
a new connection to a location to draw magical energy from, so you
note down “the grove behind the village”. Then when you want to cast a
level one spell you can call upon that location to help you do that.
On the symbolic layer of the mechanics, it works exactly the same as
slots did before. It’a just an added layer of description connected to
each one. This would be similar to the Magic card game (especially as
expressed in those old Shadowmage comics), or to the Magic Carpet
video game.
Of course, in many D&D settings inspired by The Dying Earth by Jack Vance, it’s that spells live in your mind and once they get out you forget them. It’s also described vividly in the first couple of Discworld books. Vance and Pratchett are so good, it made me fall in love with vancean casting. So slots are just “the space in your mind dedicated to remembering a spell”. You woke up, memorized a lightning bolt, another lightning bolt, and a light.
3e introduced a classes “sorcerer” (and Pathfinder added the divine equivalent “oracle”) that used a slot system. In a mindbogglingly flavor-killing move that defied all laws of Vorthos, they decided to call these flexible memorizations “slots”. As in: a normal wizard would write down three spells they were gonna cast that day. A sorcerer could leave those three lines as blank lines, as “open slots” to fill with anything.
Then when 5e made all casters work that way, i.e. they made wizards work like sorcerers, one would think they would’ve just thrown the sorcerer on the Warlord trash heap, but they cooked up the spell points system for it; playtesting showed that that didn’t work very well and the time for release was nigh and they had promised all old classes would return so they reverted to the normal slot system, slapped some metamagic on it and shipped it, and relegated the spell system to the DMG where it lives on as the variant we all know and hate (because how cumbersome and cross-river-to-get-water it is: you still have to use slots, it’s just that you spend points to get slots. So instead of replacing a complex system with a simple one, you now need to learn two complex systems and how to constantly translate between them. Not into it).