Similarities Between Two
In Undertale, Papyrus is a boastful guy. He has an obsession with spaghetti thanks to Undyne teaching him to cook. His "battle body" is just a costume he wore to a costume party weeks ago and never took off. He gets really into character. Similarly, the Warrior does not take off his costume even to be treated for his pizza-related injuries. The bandages are depicted over top of the mascot costume. The Warrior even borrows Papyrus' iconic phrasing when he speaks of himself: "I, THE WARRIOR..." They also both speak in captial letters (mostly; the Warrior sometimes uses lowercase.)
Hiding in Plain Slice
The evidence to suggest Papyrus inhabits the Warrior is plentiful. Of course, Papyrus is busy. This would line up with him working full-time. Sans also does not call him by his name, perhaps due to Papyrus becoming one with the Warrior (and Sans perhaps being embarrassed of his brother). Sans also says he will "check his schedule" when asked about Papyrus. Additionally, there is a deflated ICE-E costume underneath Papyrus' sink in Undertale. It can be seen when going to challenge Mad Mew Mew on the Switch version. The only other time ICE-E is referenced in Undertale is on the word search puzzle that Papyrus leaves for Frisk.
Also... ICE-E'S is blue now.