I would say it’s an outdated look, not an updated look. A wide open counter with room to spread out would make it easier to work. I do like the idea of the mixed materials, although I know many are not.

I used to have a split height island. The pro was that clutter was hidden. The cons were that I lost counter space and that the higher part of the counter was really too tall to use as a bar. I agree with Jmm above.

Your designer is stuck in 1999. The kitchen's only real need for change is the countertops and black appliances. Everything else is pretty up up date. The cabinet color and wood floors especially. Even the counter color is perfect. It's just tile. Replace that with Corian or Quartz, and it would be great.

In our previous home, I had a split height peninsula, but I also had an island. In your kitchen, your better with one level, IMO.

I think you need to find a new designer, if the one you’re working with says to do a 2-tier counter in that space. Really, find a different one. Be thankful you get the red flag now, before you’ve spent money.

Your kitchen ceilings look low when compared to your open living room. Raising part of the the counter is going to make the ceilings appear even lower and will close in the kitchen. I would keep it all one level.

If your designer thinks a split height peninsula is more up to date....oh boy! Plan a 15” overhang if you have seating.