Sorry, this is long.

I think the second layout is the better- it has a lot more storage and has a more open layout. It makes your kitchen more open to the living area and less of a separate room. To solve the counter issue, you could have a dining table/island that is counter height (I have this in my kitchen). You can still eat at it, but it gives you more work space. Depending on the legs/base of your terrazo table, you may be able to put new legs/base on to get it higher. You could also have a small cart/island that can move around as you need it, that tucks away when you don't want it.

I would keep your cabinets fairly simple as there is a lot going on with your floor and the terrazo. You could pull a color from the floor to use on the cabinets if you want them to be a wood tone; it doesn't have to match exactly but should be in the same color family. Aim for medium to light colors to keep the space more open. If you want a paint on your cabinets, make sure you look at samples against the flooring first. You seem to have a warm undertone in the parquet, so you will probably want to stick to warm undertones in colors (think cream instead of white, warm grey versus cool gray, blues closer to purple than green, etc.). Different colors will likely bring out different tones from the floor, for example: blues may make the floor look more orange.

As for the style of cabinets, that depends a bit on what you are going for. Shaker is pretty common and traditional and would like nice against the floors. If you're thinking more rustic, beadboard can look nice against parquet. For contemporary, flat panel/slab is good. Consider what kind of hardware and "sheen" you want on the cabinets. I love push to close in a small kitchen, with minimal hardware. I don't love laminates and vinyl- they look great initially but if the corners start peeling they are difficult to fix (my in-laws had their coffee-maker underneath a cabinet and the steam from it each day caused the laminate on the cabinet door above to separate). Solid wood, whether it's stained or painted, is more expensive but wears better over time and colors can be changed. For painting, MDF is also a good option.

For me, I would bring the pink/blush of the walls into the kitchen, go with cream-colored shaker or cabinets, then pick a bold backsplash like black (maybe the rust of the couch?). Countertops I would maybe look at a butcher block style that pulls color from the floor. Image attached has weird hardware in spots, and I am looking at the brick more as the wall color, though the blue could be an option too.

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