Is that blue wire at the furnace also available in the wall behind your thermostat?
If it is, the fastest and easiest way to fix the problem is to connect the blue wire to C on both sides and remove the C adapter. (Then reset your thermostat and remove and re-add it in the app.)
If it is not available, you need to find the point that the Y wire is spliced to send the signal to your compressor and remove the splice so that the furnace has an uninterrupted run of wire to the thermostat. Then you need to wire in the compressor directly to Y and C on the furnace board.