The “front” or “forward” direction of a screw is clearly the face of the fastener itself, be it a hex head, Phillips, or Slotted screw.

Correct.

Picking a side of a face as the front doesn’t make any sense.

Right. Nobody is talking about the under side of the fastener. Just looking it the face of the fastener, as one does when driving into something.

The whole thing needs to rotate one direction or another,

Wrong. A rotating circle rotates in all directions, including right and left, up and down, at the same time. If you attach an arrow perpendicular to the circle, pointing in the direction of rotation, then (if rotating clockwise) the arrow will point right at 0°, down at 90°, left at 180°, and up at 270°

and it will either rotate to the right to tighten, or the left to loosen.

You’re talking about the TOP of the rotation. The bottom of the rotation is moving the opposite direction. Just like the right and left sides move in opposite directions.

Think about a wrench hanging off a fastener, handle pointing to six o’clock. To tighten it (clockwise), does the handle move toward your left or right?

No it’s the face of the clock, and the hands rotate around it to the right.

From nine o'clock to three oclock it rotates to the right. From three to nine it rotates to the left.

The rule for the top of the rotation is “righty tighty”. For the bottom of rotation the rule is “lefty tighty”.

The “righty tighty” saying doesn’t specify which side of the rotation it’s referencing, which as a kid helping my grandfather in the garage was confusing.