It’s hard to tell from the pictures, but it looks like the cable with black/white is the pressure switch, one lead to L1 and the other to the coil. Check. But I don’t see any control wire connection to either L2 or L3, which should go through the OL contacts to the other coil terminal. It almost looks like the 2 wires leading to the OL contacts both land on the other coil terminal.
Again, hard to tell for certain.