How to deal with this strange Nimzo-Larsen system?

Recently, I played a game as Black with the following opening moves: lichess.org/eEejR1tv/white#17
After seeing some theory on Nimzo-Larsen, I came to conclusion that this is not how this opening is usually played.
So, how do I deal with this system? Any ideas?

The database says that Black should play either 4...d5 or 4...d6.

4...d5 is logical because after 4.c4 White has taken the game into English Opening territory, more specifically the Reversed Sicilian. The early d5-break gives Black the same resources as it gives White in the Sicilian: plenty of space, a centralized piece, an open line for active piece play, &c.

After 4...d6!? Black intends to fianchetto his dark-squared bishop and play the position like a KID. A decent choice if you play the KID against 1.d4.

What's the point of ...Bc5? Is it looking at the pawn on e3? Restraining d2-d4? I doubt if black can entirely prevent d2-d4, but there should be time enough to prepare a hiding place with ...a6 before d2-d4-d5 becomes a threat.

I like both 4...d5 and 4...d6, as @forsoothplays recommends. I used to play the KID and other fianchetto defenses when I was younger, 4...d6 followed by ...g6 appeals to me. Two very different types of middlegame, each with it's own set of possible plans.

Don’t play it.

Thanks for your opinions! Yeah, Bc5? was probably a bad idea, but I was a little bit confused to see such an opening at the moment :).