The player is in fact diegetic to Undertale.
Here’s something from my FANDOM days, but altered a bit to make it a bit clearer.
Now, to start with, we know in Deltarune choices being done with the SOUL is because we, the player, who control the SOUL, is the one making these choices, distinct from Kris. The same system is used in Undertale. …But okay, maybe that’s just a stylistic choice. Sure, Deltarune was planned before Undertale, was planned to look like Undertale at first, and Undertale was planned with Deltarune in mind (Like the Gaster easter eggs)… but maybe we’re looking too deep into things?
Then we have Chara. In the official Japanese translation switches from hiragana, in the main game (As the narrator) to kanji during their final speech at the end of the Murder Route. But again, maybe we’re looking too into this. Maybe it’s only there because Chara is much, MUCH more serious in that speech.
But, here’s where we run into some real hard evidence. If you do a second run, Chara wonders why we’re continuing to recreate and destroy the world. That there’s something about us, some kind of perverted sentimentality. But… doing a Murder Run and restoring the world is like a True Reset. The cutscenes act as if we haven’t done it before, and Frisk doesn’t remember their previous murder runs. They don’t automatically shake Sans’ hand, they don’t do any of the things they usually do when going through things they already did. Yet, the person Chara’s speaking to is presumed to remember. That only leaves us. The player.
Now, let’s take a look at Undyne’s date. There’s a few cases where Frisk’s personality shines through past ours. For instance, if we attack Undyne during her fight and do a real attack, it still only does 1 damage. Frisk has no intent to attack. But the real smoking gun here is the soda.
Frisk… doesn’t like soda. When we try to inspect it with Undyne there, she can tell through Frisk’s expression that. (Much like characters in Deltarune can tell how Kris feels from their expression.) And if we try to make Frisk choose the soda as their drink…
Undyne:Oh, soda? Actually, even though you pointed to it, you don’t look happy.
This expression doesn’t happen for any other option. If we’re supposed to be Frisk, this makes no sense. Clearly we picked soda because we wanted the soda. But Frisk… doesn’t. They’re doing the thing where they do what we tell them to do, but not the way we would have wanted. They get to decide how they do it, much like the dynamic between us and Kris in Deltarune.
We’re not Frisk. We’re our own entity, that just so happens to be controlling Frisk. But… how?
At the end of the Murder Route, Chara asks for our soul. We give it to them to restore the world. And at the end of Pacifist afterwards, they get to possess Frisk. But all that changed is they have our SOUL. That tells us the SOUL can be used to possess Frisk.
Now, it would make little sense for Chara to somehow reach beyond the screen and steal our real-life SOUL. It really makes more sense for them to be taking the SOUL Frisk has. And taking a look at the filename for our SOUL during Flowey’s right, we get our_heart.
My_[###] is generally used for things owned by Frisk. my_room for Frisk’s room during the post-credits scene in Pacifist. “Our” would imply Frisk… and someone else. Flowey doesn’t have our soul yet, so it’s not him. This should remain the same regardless of whether we did a Murder Route first, so Chara is off the table. Plus, Chara was awakened from us, not Frisk, there’s no reason to suspect they shared a SOUL with Frisk this whole time. This is the player’s SOUL as well. And it’s how we control Frisk. And, even further, it’s how we connect to Undertale’s world in the first place.
In Deltarune’s Goner sequence, the SOUL is the first thing to appear, and Gaster asks if we’re connected. While Spamton wants the SOUL to look into [HEAVEN], a whole deal of its own, but this seems to imply Spamton gets to see something if they had that SOUL. It being the connection between us and that world would explain this elegantly.
Also, in the XBOX version, if we unplug our controller in the True Lab, we have a whole bunch of “No ### is connected”, with various body parts being mentioned, presumably Frisk’s. There’s a connection between us and Frisk. And, again, the SOUL is consistently used when selecting options. Even the game’s shortcut icon is the Red SOUL, and we know Undertale and Deltarunr were being worked on at around the same time, and there’s plenty of evidence there of the SOUL being a connection.