The columns won’t stand up and be stable by themselves. They need to be attached to each other, and to the island cabinets, with stretcher bars. If you use 3/4”x3” wood stock vertically, and put in a few cross pieces in between, like a ladder, to create a gridwork system, then that should be fine for support.

The critical connections will the the ones where the stretchers attach to the cabinets, and each other. Glue and screw with pocket screws into something substantial enough, and it should work.

The trouble is, that cabinet side does not look substantial enough and may need interior reinforcement for any type of support to work. Are no decorative door panels planned for the sides? I would have liked to have seen that been integrated into the cabinet build. It would be more aesthetically appropriate and much stronger.

At this point, it may need an applied piece of plywood to the interior, glued and pinned. That will give enough meat for attachment, and be stronger against buckling. And you need blocking at the toe, directly under that, to transfer the load to the floor. The cabinets, and the posts, also need secure attachments to the floor. Not just gravity.

If extra support suggested then

For extra precautions & peace of mind do all that is suggested by the pros.

Very strange island.

If you don’t understand cabinetry components enough to understand what I’m talking about here, then you need to hire someone who does. I’m not talking about anything on top of cabinets.