The blue wire at the thermostat is likely connected to the transformer in the air conditioner. Do you have 2 sets of wires in your wall behind your thermostat?
Also, on the furnace board, it looks like green used to be on G , yellow used to be on T, red used to be on R, and white used to be on W, but when you re-wired it you connected white to W, red to R, yellow to Y, and green to T.
Now, T is the same as C, so without a C wire, you would need something between there and the thermostat, but the lack of a Y wire at the furnace in the original wiring isn’t great. Does that yellow wire at the furnace enter the same wire bundle as the rest of the wires? You might need to open up your air conditioner and take some pictures of the wiring there for me to be able to help you.
You might have a series wired air conditioner, if you don’t have 2 sets of wires in the wall behind your thermostat.