HOW TO RUN: DELTARUNE
So! Deltarune, if I were smart I'd have written this around 2 or so months ago! Unfortunately, you're stuck with a lazy writer, so sorry!
Now the thing with Deltarune is that its an "Ongoing" game, we don't really know what its really about thematically, or how a lot of its plot beats are gonna fully pan out. So I'm gonna instead focus on games that can replicate vibes and the idea of travelling between two worlds to have adventures in them. Cool? Cool
GAME 1: Eidolon 2e
A theme you'll catch on quickly here is that a lot of TTRPGs that can handle Persona can also probably do Deltarune, similar rough concepts!
Eidolon 2e is... the exact half way of Jojo and Persona. A core concept within the game is the idea of the Undertow, a realm of reality below our own. The game deliberately doesn't specify what the Undertow is, so the players may come up with their own definition of what it is. The game is generally, very fun! the card drawing mechanic that fully eschews die in return for a more "manipulable" system is extremely Neat. Its a game I highly recommend checking out if you want something like it.
As for Deltarune, its pretty easy to reskin the Undertow as the Dark World, and some of the playbooks lend themselves pretty strongly to specific Deltarune characters, and if they don't, then the game has a fairly sizeable homebrew community with some fun projects you can check out.
GAME 2: VOIDHEART SYMPHONY
Voidheart is, also, a persona inspired TTRPG with a strong focus on dungeon crawling through dungeons known as "Castles", which empower and absolve the rich and powerful from any and all consequences for their actions. The void can also have dungeons called "Prisons", where the host is unwilling and will be killed by the void if the players don't collapse it
The primary reasoning for Voidheart's inclusion is the very strong divide between the City sections and the Void sections, effectively playing as two separate games with separate mechanics, the game also just HAS an acting system, characters can choose to spare most of the enemies they defeat, even the bizarre void creatures they encounter in the castles. This game is one of my favorites! And since I recently picked up its Revised edition, expect some more about it sooner rather than later, I think you should absolutely check it out even outside of it being a good game for playing Deltarune in.
GAME 3: Girl by Moonlight (Frankly, any Magical girl system could be here, this one's just my favorite)
Deltarune at its core is a little bit magical girl media, but GBM specifically has a bunch of different cores which can run different magical girl stories. For specifically Deltarune, I'd imagine either the Maze of Dreams core (which focuses on exploration of an alternate world created by mass consciousness) or Beneath A Rotting Sky (Which focuses on powerlessly fighting back against an apocalyptic prophecy) would work best. Honestly not much to say here, a lot of magical girl systems would work for it... frankly some mecha systems might even work. A Strong divide between the Hometown and Dark World segments is, in my opinion, fairly important for telling this sort of story
GAME 4: Fabula Ultima
Probably the most dubious one in here. Fabula Ultima is inspired by the very things that Deltarune is parodying, while you'd likely lean in more on the Combat side of things in this more than any of the other systems mentioned here, you COULD very much play a deltarune-inspired game in this.
Conclusion
There are some TTRPGs that are more directly meant to be "Deltarune but as A TTRPG", but A lot of them I found were kinda lacking, or just unfun, so these are some personal picks from my backburner. Personally I think the best experience you'll have is with Eidolon 2e or Voidheart. but the other 2 would also work great! It really depends on what kinda game you like, and what experience you want from a Deltarune-inspired campaign.