The computer says 13...c4 is an inaccuracy, but in reality it's a positional blunder. It closes off both of your bishops, and basically locks up the queenside.
There are some basic (specific) positional ideas you can learn about closed positions, but keep in mind:
*You won the game anyways. It's because your opponent hung something, then allowed a 1 move mate. It's the most important thing at this level, and you need to master playing tactics and avoiding tactics from the opponent.
As Cherub already explained, c4 doesn't open up the middle more, since it allows b4. IF it actually opened up the middle, than yes, you have the two bishops, so that would likely be helpful, depending on the position. You do not have a lead in development at all as you stated. You are not castled, and developing the knight to h6 (the only square right now) requires serious thought since it will likely lead to bxn in two moves.
What you should be asking yourself here is "how am I going to complete development and castle safely" and "is nh6, nf1, 0-0 (or keeping my king in the middle and pursuing something else), bxp pxp OK given that my kingside pawns are wrecked? This is a seriously tough issue for even stronger players. These king of decisions do come up in the French Defense advance variation, but at this point, the position is irregular and needs to be specifically analyzed rather than relying on the generality that nh6 and bxn is often nothing to fear for black in this opening.
I tried my best to stay calm here, but I have very little experience with very closed positions. I opened with the Scandinavian; however, it quickly transposed to an advanced French, and I don't play the french.
The "big think" I had that consumed more time than how long I've spent on turns usually was on 26. Bxg5. The thought process I had was "Well, rooks like open files. I can get my queen on the same open file as my rook, both on his king side, while all his pieces are on the queen side. Let's try it". Had no idea he'd blunder his knight.
My really crushing and weak start had to be my wasted bishop movements.
I'm not sure how I should've played my early development. I also feel like I don't understand how to use my pawns better. Hoping people can elaborate on the pawn point in particular, because his pawn push on the queen side felt oppressive.