I see plenty of replacement manual window gears like pictured below, but what about the gear that drives this gear? Do I have to buy an entire window regulator set?

I'm asking because there is a lot of slop in the driver's-side window crank handle, and before I get into it, I'd like to know if it is likely that only this gear needs to be replaced, or is there a chance that its drive gear also may need replacing.

Does the AIM have a part number?

I'll take a look at the AIM tomorrow.  I've looked at many of the vendor sites but none show the actual gear.  On some I can see that it is part of the rest of the window mechanism.

It looks like it is just part of the window regulator assembly.

You can buy the window regulator crank shaft as a separate part. It interfaces with the gear.