A fuse will seldom smoke when it blows. You may hear a faint “tick” sound sometimes when a fuse pops.
These failures often happen in a chain. Worn blower motor draws more current which can in turn burn up the resistor pack or blower module, fan speed switches, and fuses. Odds are the resistor pack is failing/failed and it could also be that the wire connector at the resistor pack has burned from long time high current draw of the blower motor.
I suspect the smoke, if not from the blower motor, came from either the resistor and/or the wire connector at the resistor. My assumption is that if the connector at the blower motor is burned you would have noticed it.
It’s possible a set of contact points in one of the blower relays could be stuck and causing the fan to run even in the OFF position. Tap the relays firmly with a screwdriver handle and see if the fan stops.