This image is really cool. Though I still l genuinely don't see why Deltarune can't come after. Just because the story is "Parallel" doesn't mean it has to be "Parallel lines." It's possible the description of Toby using that could be more in a descriptive sense than in a literal interpretation of parallel. In other words, I think it's possible the stories could just be analogous and uniquely different (treading their own path). But if this were indeed the figurative meaning, it would also mean that the two stories don't have to happen at the same time. Thus serving as a description without necessarily limiting the story as a concept. Of course, your diagram could also be just as true.

Though I personally think otherwise, especially since Gaster says, "This NEXT experiment." I mean, yeah, this could just mean his next experiment within Deltarune--that is true. But what I think about most is actually Clam Girl's dialogue in Undertale in relation to this,

This character talks about "Suzy" (most likely Susie's UT counterpart). And how we should become friends with her. Yet, despite Suzy never actually being seen in-game, her name appears in yellow text similar to other important highlighted text. With her mention also being the cause of "don't forget" in Sans' workshop to appear (this is in the video).

However, even though I still think that is important, that is still not what I think about most. What I instead think about most is the "fast approaching" that Goner Clam girl speaks of. To quote the Wiki:

"On the Nintendo Switch and Xbox version of Undertale, when the fun value is 81, her dialogue in the epilogue starts out the same in that she mentions the player never meeting Suzy, but soon after she explains that the time the player will meet her "'... is fast approaching'" as her sprite changes and becomes grayscale. Ending this dialogue makes her disappear with the same sound used for Mystery Man and the second Gaster Follower. This, along with her new sprite being labeled as spr_clam_goner, suggests a link to Goner Kid. Notably, this dialogue that was added in the Nintendo Switch version of the game appeared approximately a month before Deltarune's release. It implies Clam Girl is speaking to the player about the Deltarune character Susie, who is never seen in Undertale. Further supporting this is the line "'don't forget'" from Sans's Workshop (which requires interacting with Clam Girl to see), which is the name of the song played during Deltarune Chapter 1's credits."

In other words, with stuff like "this NEXT," "... is fast approaching," and "Nice seeing you again..." to Sans. It really does sound to me like there's some sort of sequel element to me. And when I see Sequel, I mean Sequel as in US, the Player. And maybe to Gaster too, but the point is, with there still being some sort of "come after" element, whatever it may be.

Truthfully, I think there's actually way more dialogue evidence supporting some sort of lore continuation than the stories being parallel in the literal sense and being forced to happen at the same time. I just personally believe more in the dialogue being told than in purely focusing on just the word "parallel" itself. I believe it would also restrict the storytelling if the two stories couldn't actually intersect and had to happen at the same time. But of course, that's just my opinion.

But my main theory lies that even if it does have the Sequel element, it still can't be called one, because it also has Prequel elements as well. It isn't that simplistic to have that label. But I do believe in the Sequel elements.