I don't think it's necessary. If you decide to add them, make sure they aren't so big that your knees knock into them as you get on / off a bar stool.

I'd let 1" square tube, steel or aluminum, into the wall and the cabinet backs and screw the square tube to the back of the cabinet fronts. And I'd use at least 6, not 3, for a span that long. Shim to level and flat please. Cap the exposed tube ends and paint the exposed flat black.

You can't screw steel-on-the-flat, no matter how thick, to the pony wall plate and think it's going to do any work without tying the wall plate into the studs with structural connectors. I don't care what the bracket manufacturers say. When they've fixed as many of these as I have, they can talk to me.

Have your fabricator use the cantilever as a bench for his crew for lunch. If he's unwilling, it ain't right.