Oh, I see. My apologies, I misunderstood what we were looking at. I thought the framing we see was the entire wall, but it’s just non-structural framing on the interior behind the plasterboard to allow space for wiring.

I am not familiar with this style of construction, so I won’t guess at best practices for hanging cabinets on it. But I would imagine that as long as the wall we see is sufficiently secured to the structural wall behind it, you should be able to hang cabinets. To be safe, you could anchor into the wall, but I don’t know enough to say how to do that without interfering with insulation or vapor barriers.

That link is extremely helpful. It seems like you’re fine to attach cabinets to the wall after drywall. The osb is tied into some serious wood framing behind it, and as long as you’re using fasteners that reach into the osb, it should be about as solid as you could want.

The kitchen metal grumpydaddy suggested isn’t expressly needed here, but that’s the most I’d consider doing to it.