What is the appropriate way to wire a 2-way switch with 3 black wires? It appears the additional black wire is for the rest of the circuit (this is not intended to be a 3-way switch), should the hot black and additional black be pigtailed?

 

2-way switch is what they call a 3-way switch in the UK. The term is not used in the U.S. Most people just call it a regular switch, SPST. Lazy man wiring. They used the less reliable back stab as a splice. The wire in the back stab and on the screw associated with that back stab should be connected to a pigtail and the pigtail* connected to one of the screws of the new switch.

*Pigtail: A wire 6"-8" long the same color and size as the wires it is connected to.