How to stabilize half-wall below an interior portal?
First, you'll want to place double studs on either side of your opening (currently you have some on the left but not right, as viewed from the kitchen). Then add horizontal members at the top and bottom of the opening, fastened into those studs. This will add a lot of rigidity by preventing the knee-wall studs from swinging left/right/out. Finally, add some screws through your drywall to the new structural members.

If you're keeping the plumbing/electrical chase in the center, the framing of that will offer some more stability.

Because one side of this wall is in a kitchen, there's also the possibility you'll attach cabinets or other built-ins to this wall. If so, those will add some further rigidity by essentially bracing the wall against the floor.

If those aren't enough, you could add horizontal or diagonal bracing to the wall, or even expand it into a double-stud (wider) wall. Those would be more extreme measures, and I doubt you'll need them.