Wiring up MLCS #9072 Safety Motor Power Switch.

[dbhost]

Since the PE bar is not connected to anything but just floating, you can freely use it to extend your ground bar if you wish. But in reality, jumpering it to the other ground bar uses up one screw terminal on each so I don't see any gain. If you want to ground your table frame then you will probably be best putting two wires under one of the screws.
Or the ugly solution of three wires into one appropriate sized wire nut. Three of them the incoming ground, load ground, and the table ground and not using the bar. which is apparently not connected to anything.

Yeah, the ground bar in the box itself doesn't make sense. For example a standard light switch, you have your load, and line, grounds are tied together and connected to the ground lug ON the switch. This thing is lacking the grounding lug. I have no clue why / how this gorund is supposed to work except that it looks like the line and load ground lines are tied together...

[LCHIEN]

That all its for, to tie the line and load grounds together. The box is plastic so nothing to ground. You could just do the tie with a wirenut. I think you are overthinking it.

[dbhost]

LCHIEN you are probably quite right about overthinking. Wouldn't be the first time...