Deltarune Papyrus Theory:
Since 2018, I've personally theorized that the Papyrus of Deltarune is a very different person from the Papyrus of Undertale.
There was always this weird dichotomy with Paps, where he could be simultaneously very sophisticated and very child-like. I thought that perhaps he was the one who built the dimension-hopping machine we find in their house as a way to escape the Roaring, but the jump between worlds took his memories, leaving him as the innocent fool we meet. Think about it: between the lazy joke-cracking Sans and the obsessive workaholic Papyrus, who would actually be more likely to build something like that?
This would explain why Sans can't fix the machine and return home: he doesn't know how. It would also explain why Papyrus is so obsessed with staying vigilant and "capturing a human" in Undertale: in Deltarune it's said they very recently moved to Hometown, probably because the timekine-monitoring devices Sans refers to in Undertale detected that's where we were going to arrive. Papyrus can't remember why it's so important to him that he waits for this human to arrive, (and possibly to capture it) only that it is.
Sans could try getting his brother to remember, but Papyrus is happy in Undertale; probably happier than he ever was as a doomsday-prepping scientist in Deltarune, so instead Sans looks after him and keeps an eye on his various timeline-scanning devices on his behalf, having long given up seeing his home again.