Depending on your goal....beauty?it could be a lovely art piece(tall and slim) ...or function? A corner cabinet for shoes , bags ,coats?...these days home represent a place to relax and rest so I am of the school that the first thing you see as you enter should set the tone of your home,makes you smile ,or feel good

Bring the window down to meet the cupboard. Really lefty47 was right about not drawing attention to it. It is a source of light ,,, so no need to clutter it up. But if you took the colour out and painted the top of the cupbard to match the wall it ceases to draw attention to itself. Just because it is a horizontal space does not meant it needs something put on it. Note- With the cupboard being white, it also draws attention to itself … perhaps take that to the wall colour too and lift the pendant a smidge. So your pendant is the feature there. The cupboard … do yo need it? One way to remove what you are calling dead space is to get rid of the cupboard.

I would embrace the element, but I would get rid of the wood chips. I'm thinking back fist sized river rocks. Then I would get a tallish flowering tropical such as hibiscus and add a few ivy plants to grow between the rocks. Additionally, a small water feature might be nice. For me, the bigger problem with the entryway is the door. You have an obviously contemporary home, yet you have a -very- traditional door. I would want a wood door with some sort of art glass element in it. The wood would of course need to be stained to match the existing woodwork. The door will be some big bucks, but it would remain regardless of flooring changes. These two doors are not specific recommendations, but examples of the type of entry door I have in mind. Best wishes!

I agree with havingfun, thicken the supports and have something growing trailing up them. I didn't even notice there was a pergola until the close up. Right now it blends in too well with the house color, consider painting it a different color. I don't know your usda zone but classic climbers for a pergola include clematis, wisteria, grape https://www.houzz.com/photos/santa-ynez-valley-mediterranean-porch-santa-barbara-phvw-vp~2485412 or go for a modern look You can also hang string lights, planters or something from the beams. Also agree lighten the front door.