It sounds like I need to reset the air gap on the A/C compressor, but I’ve never done this before. Do I do this by adding shims or is there an adjuster screw/bolt?

borrow the a/c clutch puller tool from Autozone-- clutch is pressed on-- no shims--needs a puller to move it..here is my cut and paste on your probable problem:

This sounds like classic v-5 clutch drag- the air gap has tightened and needs to be adjusted back to .020" . I have answered this several times- and usually see about 1 a week during the hot season. The noise is a scrapping/rattle only with a/c off- should see signs of metal shavings about the clutch hub. The fix is to borrow the installer/removal tool from autozone and back off the air gap a tad. This can be done on car, without removing compressor or refrigerant, and can even be done without removing the shaft nut since the nut does not bottom on the clutch drive. Pull back the plastic cover in wheel well to access

Thanks!