When I tell you that I don't see a significant difference between the red SOUL controlling Kris, and their acting "on their own" alongside or independent of it, I need you to understand that I mean that literally. They are the same just as you're the same person on your best and worst days, and that is both one of the beautiful parts of the game and also a key source of its horror.
Yes, as the player You have input and probably opinions outside of Kris's usual experiences. This is no different than many other player characters you ostensibly control, yet lack the same knowledge they do. This is a useful tool video games can use, such as by not telling the player the real motivation for a player character (ex: Braid) so they can better play a role that the average player can't be expected to portray on their own.
In Deltarune's case, Kris's role as both a mystery to the player and at times an adversary, is at the core of that player/player character relationship. They are quite literally living a double life, with competing motivations that only become more diverged as the game progresses. They wrestle for control because they are bound by both paths, and full of contradictions. They're creepy and anti-social but when they speak people take notice. They resent being tied to the strings of fate, yet truly care for Susie (and potentially Ralsei) who they've gotten to know because of it.
There seems to be this pervading sentiment in the Deltarune fandom to try and figure out the "real Kris", in the most parasocial way possible (not that it's at all correct to use the term for a fictional character, but that's really what it feels like sometime). Using these choices or this flubbed dialogue delivery or some other reaction that other characters note, all in the name of figuring out what Kris is "really" supposed to be like. This is accompanied by an almost self-deprecating attitude that whatever choice you make in game is also the "wrong" one, as far as Kris is concerned. Believe me, I was there myself once. It's silly in retrospect.
And while it's true that Kris is not a self-insert in the way many other silent protagonists are, at the same time if you look up 1000 fan works on Kris, you'll get 1000 Krises(?) within. Each one colored by that person's unique experience playing the game and trying to be Kris (a task which is impossible by design as there are always cutscene moments where You and they diverge entirely).
Yet those choices and that play experience still goes into building that person's impression of the world of Deltarune, and the characters therein. That's why you play as their SOUL, so you really feel the moments when they are at odds with themselves, so much so that they separate entirely (a neat trick that so far has had precisely zero explanation, and I still like it that way). If Deltarune were a non-interactive medium, their SOUL would simply be featured as one more part of who they are, something visual for an audience to latch onto what internal conflicts in a troubled, emotionally damaged, definitely mentally ill dysphoric teenager might look like.
Also if I may be real here: this is something I feel many people can understand on some level, and that's why so many fanworks play in this space where, intentional or not, Kris and the SOUL blend together in weird fun ways. Sometimes just as a visual symbol of Agency, or Control, or Impulsivity. Many times the SOUL will go unacknowledged, simply assumed to be there, yet the characterization is unquestionably Kris.
It's when it comes to portraying the relationship in the opposite way—the Possessed By Eldritch Horror angle that fandom is obsessed with—that it gets muddy. With how much everyone assumes this to be true, in practice it actually has to be handled in fanworks delicately so to not be completely tonally jarring. Which is appropriate because, while I don't believe it to be true (at least not in any overt way that the game will either confirm or deny someday) the dichotomy of player/Kris control is still subtle in game, compared to what it could be. In truth, Kris doesn't act like someone possessed 95% of the time. They act in cutscenes like they've been walking around on their own all day. Nobody with the sole exception of Noelle (who is not herself a reliable narrator) ever questions whether they're in control of themselves, outside of being "weird" or "not feeling well".
You can really see this in contrast when fanworks that aren't subtle about depicting Possession Theory take a nose dive from what they were really about to remind us of the meta-dimensional parasite that the author made up inside of Kris. Like, you can really see it when people write pre-canon scenarios about Kris and the Bunker Gang's motivations, and when they stop talking about characters and start spouting about nonsense player-inserts. "Kris, I have something very important to tell you, and you can't tell another soul: I've found my daughter. I've found December, but she's changed, not herself. I need you to help. I know how guilty you've felt about her disappearance, but together we can bring her back. You will need to coordinate with the darkened shade she has become, I trust you can handle yourself in that regard. The ritual required will involve following the Prophecy, which means your SOUL will be needed to purify that darkness, when the time comes. Also you will become host to an eldritch being that can puppet your body and will basically live your life for you the next few days, the necessity of which will all be explained later, probably."*
Like, there is nothing that takes me out of the story's immersion than this SOUL parasite talk, it's nonsensical and I hate it. I know, no accounting for taste, but you have to admit this comes from nothing other than trying to justify a hypothetical player's input into a fictional story. Except that, it's a non-interactive fiction so, there literally isn't a player inputting anything. It's just Kris. At the very least, it should be couched in the words and perspective of the characters. Maybe they believe that by becoming the Cage in the prophecy, Kris is receiving the Angel's guidance directly, and then don't confirm or deny this in the text. It's a belief like anything else the characters would believe in.
Phew, okay, that's the harshest opinion I'm going to give here. I don't know where else to go with this, so have some fanfic recs:
No Holiday - Kris and Noelle have a talk.
Strike Out - Dess Holiday swings the bat.
Better Dreams - (unfinished—on indefinite hiatus) alternate canon/timeline starring Dess. Features the kind of meta elements I LIKE (fitting the medium of a written work)
A Soft Place to Land - Krusie goodness. From Susie's perspective, the sequel is from Kris's. Both are excellent.
Flirting Lessons - PEAK PEAK PEAK! An unapologetically messy af krusielle story. Also a great example of a fanwork handling the SOUL in a very subtle manner.
BURNOUT.ogg - Simply fantastic character study of Dess and Kris's bizarre relationship. One of my favorite Dess depictions too.
st-krisis.log - Prequel to BURNOUT, from Kris's perspective. A bit of a challenging read with the verse format, but super rewarding.
*by the way this isn't any particular fanwork I'm calling out, but some variation of this definitely comes up more often than you might think. I was even generous in assuming the author treats it as their own SOUL, and not some transplanted other human's SOUL or demon or whatever else that's based on nothing.