Do not use a tension rod (like a shower curtain rod). They are not designed to hold continous weight of clothes. Either a wood rod cut to length with screwed to the wall hangers or a steel rod, cut to length or two piece extendable. Shelf above or not, just depends if you think it will be used.

Make the rod high enough that full length dresses or other items can be hung to dry without touching anything else.

The room seems quite dark. Maybe think about adding under cabinet lights, an diffused LED light strip on the top of the cabinets to provide reflected light above the cabinets (use a dimmer), etc. Just being brighter will make the room feel less depressing.

I’ve been using a tension rod for over a decade and it is fine for everyday use. We wear a lot of high tech fabrics and of course my husband likes his fancy pants undies that can’t go in the dryer. We actually have 2 drying racks plus the tension rod, some of my jeans that have a lot of stretch in them go on a drying rack.

You have a good idea with the rod and shelf, you can get a set like your photo or I'd probably go with separate pieces in white. You can add color decor on the shelf to coordinate with a rug and the rest of the room. Just be sure to check your rod and shelf measurements, the shelf depth shouldn't block the lighting above, and the rod depth should be hold a coat hanger which needs 24". Also consider the height of the rod - you want to be able to reach above to hang clothes comfortably and still allow space at the bottom so you aren't accidently sweeping items off the countertop.

The tile would be pretty or you can hang artwork for the days when nothing is hanging on the rod.

I’m a man. It looks great the way it is. Add a framed antique picture or some knick knacks.

Add some crown moulding on the ceiling to visually enhance the room?

Border stencil to simulate tile? If you paint use light colors. They make small rooms feel larger

RUBBED

One crazy phone! Still add something green to the brown countertop and if you put that on the wall hopefully you don't get tired of it cuz otherwise you're peeling your drywall

Stack in the back right corner.

Honestly it would have been better, space wise, to put them across the back of the room. Architect probably wanted to hide the appliances from view, but this makes them hard to access.

Seriously consider putting in a stack, washer tower, something. If it were me i would put in compact units, but thats a personal choice.

Just a consideration - not sure where you fold clothes and/or hang them, but that lower cabinet could have a hanging rod above, and folded clothes on top of that cabinet. Empty space across from stackable W/D could be for laundry basket(s).