Would You Castle or Play Kd7 Here?

This position was in a recent chess.com game of mine. I was Black and won the game without much trouble due to the material. However, my chess.com friend @Gump_forest (not my opponent this game) was adamant on a particular move we disagreed in severity on. In the actual game, I castled.

A year ago I would have played ...Kd7 in a heartbeat and barely looked at castling. I'd consider it, but in the endgame I would have wanted the King in the center of the board anyway. Furthermore, ...Kd7 takes away opponent counterplay of Rc7 ideas.

In this game, I played my instinct move of castling. My logic this time was that ...O-O prioritizes King safety and I'm up by plenty of material anyway. White won't be able to win any pawns on the 7th rank anyway, but even if they do, what difference is 2 point lead or 3 point lead in material? The difference is negligible as Black still has the material lead and enough to easily convert into a win. I also know from pattern recognition (and Kmoch's book Pawn Power in Chess) that the open c-file isn't giving White enough to infiltrate and remain there (Kmoch has a small section on when an open file with Rook on the 7th rank is dangerous enough to worry about or not). 

Although I agree that ...Kd7 is slightly better, I feel like considering alternatives like ...O-O more seriously (even if objectively a bit worse here) is part of a learning curve I must endure so that I may play the best moves in the future AND know from experience why alternatives aren't as good.

TL;DR version in bold below:

@Gump_forest and I both agree that ...Kd7 is slightly preferred, but what we currently debate is how "bad" castling is or not. They claim that castling is "a careless move" and that Carlsen would consider it a "Mistake" or "Blunder" if it was played in a game of his. However, my opinion is that both ...Kd7 and ...O-O were fine moves with ...Kd7 being only slightly preferred. For me, it is playstyle and preference and Black is winning in either way - it is too one-sided enough to matter debating a few centipawns. Is castling a flat out "Mistake" here, or am I overestimating a "simple" castling?

For reference, quick engine analysis claims ...Kd7 is about -5.39 and ...O-O is about -4.80

King safety isn't an issue here at all, it's an endgame. Kd7 would have been an automatic for me.... 0-0 wouldn't have been considered. I would consider 0-0 to be careless at my level or higher, and I consider it to be a mistake from a human perspective. hope this helps! 

Obviously up a piece, it doesn't really matter. But it makes a big difference when you aren't nearly up that much material. Knowing that Kd7 in this type of position is much better instinctively can be important.  

it is not a blunder or anything I think according to Carlsen he would just be like " why are you allowing your opponent even a slim chance of play" kd7 is undoubtfully better I don't even know why you would consider castling king safety is no issue here, and it shouldn't be.

0-0 is underdevelopment because u need ur king in the battle in most endgames unless there is some danger (in this case there is none ) and u wanna contest the c file with rc8
0-0 gives counterplay for black with rc7 (not enough to hold ofc) but thats just annoying to deal with because the rook on the 7th rank just prevents us from loosing sight of the pawns and we slightly passive ...he dominates the c file with rfc8 in the future and he doubles up ...we might win that but its just nonsense...why would u give the c file and counterplay like that and chose to be passive when we have much superior option ? 
ur first instinct with ur king in the endgame should be to bring it up...then think if there is some danger..if there is then dont do it (in this case there is none) ..i would say castling as a carless move ..inaccurate is a better way to put it...
concretely u can get away with 0-0
but i would say ur instinct shouldnt be 0-0 in the endgames
there was probably rc7 rab8 rfc1 nc6 trapping the rook..
but i bet u wouldnt have thought about it and just castled because of ur fundamental flaw of thinking which is quote and quote "To complete development" ...i would say u underdeveloped with 0-0 ..and u r underestimating how huge a small counterplay for ur opponent can get ..it might not be a big deal now but after some moves u will struggle alot to win where u would think like "wait i was up a piece ,i should have won this cleanly ? wtf just happened?"  ..and we see exactly that on move 26.nxe6 +..

and an important point ...there is no point in referencing these subtle details with an engine ...they see things concretely and might think both are ok but we humans can miss things..so going with no counterplay option is 100% more logical than giving counterplay and getting out of it by concrete play...i mean wht ? why r we even debating this?

Kd7 is simply better, but since castling doesn't lose material (Rc7 Rb8) I would be inclined to say "who cares?" because truly, it doesn't matter

@gump the problem with white doubling on the c file is that black can just play Nc6

nicely put it ... ..i bet prime kaiba knows all this stuff ...he will wipe the floor with me ...hes just tired rn..but we will see    ( i still love u kaiba UWU)

i did mention it 

yeah I mean but b7 is weak its much more unpleasnt than it has to be just kd7 and rac8 its curtains.

I wouldn't say it is unpleasant if white can't even win material. Maybe I just think differently, since I'm used to playing with space disadvantages. But there's nothing white can do. Black plays Na6, brings his king back to d7 (lol) and plays Rc8. 

Sure, it's a lot of extra hassle, but white doesn't win material, and its just a few automatic moves anyways. 

that's my point lol but we are on the same page

u love to make ur life difficult ..dont u   ( says the guy who plays the dutch ;D)

I guess. It really isn't that much of a problem. Black plays five moves to achieve what he can get in one. Was it necessary? No. Does the winning method change at all? No, also. additionally, it's online chess... a few extra moves is like ten seconds. 

you play the dutch i play the kings indian

rewind to a year or so ago whenever I played the KID you would say "ewuu kid player" in the chat

try dutch ..u will get bad positions out of no where... i mean its a good weapon with ur  alekhine s defense

Changing your orientation from "Mistake" to "Innaccurate" xD but okay I see your point too.

As for why debating this...it is because you told me to create this forum thread lol 

I do not remember.

no sir, I am absolutely positive you said that.