New thermostat: How to wire it?
Noting that the new one includes fan speed control and the old one does not, I'm going to say you bought the wrong model of thermostat.

Motor speed control isn't something that can usually just be added by changing the thermostat.  It would require specific wiring and motor change in the air conditioner.

Completely disassemble the old thermostat, and examine the circuit board to get its model number and order using that.