Thermostat wiring for fan only
Your thermostat cable coming from the wall appears to have only 2 wires. Therefore the thermostat can only send one command: everything on, or everything off. (This is very common in older systems.)
In order to get separate fan control, you would need at least three wires, but at the other end of the cable, the furnace would also need to be wired for this option.
To determine whether this is possible, examine your furnace and update your question with photos of the wiring diagram (if you can find it) and how the thermostat wires are currently connected to the furnace's control board.