Compute Analysis of rook sacrifice

In this position:
lichess.org/editor/rq3rk1/2p1bpp1/bpn1p1B1/p1PpP3/P2P3p/1N3N1P/1P1B1PP1/R2Q1RK1_w_-_-

Stockfish says giving up the rook to the black bishop with bishop c2 is by far the beneficial move as opposed to what I did which was bishop xf7. As a newbie all I see is a material loss. What am I missing?

The trick is that at the moment of the game you show, you are up a piece.

So, after retreating the bishop, when black takes your rook and you recapture his bishop, you will have two pieces (bishop and knight) for a rook.

The exact evaluation of this position is a bit more complicated, though.

By raw material counts that's just about the same as Bxf7, since both would be +1 with simple material counts (3+3 vs 5 or 1 vs 0).

The reason Bc2 is so strong in this position is that most of black's pieces are unable to defend his king, so when you go for the line where you get two pieces for a rook, the black king will come under a vicious attack fairly quickly.

Count the material. Your bishop on g6 is attacked. You must save it to keep your material advantage.