You would put 2x4 underneath at the wall and metal struts ties into the studs at wall that extends out and support the counter.

Look up countertop overhang support. There's a lot of different choices out there that tied into the studs.

I would consider swapping the dishwasher with the drawer cabinet... that is put the dishwasher next to the sink, then the cabinet. Besides supporting the counter better, it would reduce the conflict between the open dishwasher door and the stool.

(6) 2" square tube steel "L" brackets bolted to the wall studs.

Is that a seam between the narrow drawer base and the DW? If so, can the seam be located elsewhere?

I would put a cabinet in the corner for more storage and support. You can move the stool to access the storage.