Are you looking to close off the area above the half wall with the cabinetry? If so, I would replace that wall with a proper wall to the ceiling. Few cabinets have nice-looking backs.

The other side has a couch. We are absolutely not comfortable placing the couch against the half wall

Yes, we are looking to close off the wall with cabinet. Was hoping to do it without actually extending wall.

Here is the back of a PAX cabinet. It's not pretty

You can get a panel for the cabinet but honestly I do not think it will look good to block off the space . Can you post a to scale floor plan to see if maybe something else could be done , maybe just nice lower cabinets with drawers for storage against that wall it the cabinets are 36" high it will be awhile before baby figures out how to climb there and in the meantime you might try to figure out something nice like the ideas from Beverly for all the time. BTW often those walls are open for a reason with heating and cooling too.