So, where is the room in question? May we see what you're working with?

It's off to the side from the living room and kitchen

Not much you can do to turn run of the mill black electronics into a Southwest look. You can do that via paint color, rugs, art work, furniture. I don't think those 2 floor lamps help elicit a Southwest vibe. Search Houzz for "Southwest Look" to get some inspiration. BTW, Mission style furniture goes well with SW style.

I was not asking for its location but photos of it. Your mood board is interesting, but how will it work in the space you have?. Please post pix of all four walls of the office room and any furniture you have that you plan to keep in it.

Share some pics of the actual space. How wed are you to the specific pieces in your mood board? (would you consider a different rug,for example) Are you in the Southwest?

You can put some of your electronics (CPU, printer) behind doors in a cabinet. You can probably also find a comfortable chair that is less office-like. Choose wood rather than a black metal shelf. https://www.google.com/search?q=wood+desk+chair&source=lmns&tbm=shop&bih=494&biw=944&hl=en&ved=2ahUKEwjV1r_8vofpAhWFb80KHQDNBu4Q_AUoAXoECAEQAQ

https://www.ikea.com/ca/en/rooms/home-office/gallery/

For southwest theme, you need to go all out or it will look half finished. A reclaimed wood desk with metal legs like this one on Overstock is 60” wide so it can handle monitors and printer and has drawer storage for printer paper, pens, office supplies. Paint the walls Sherwin Williams Universal Khaki or one of the colors on its paint chip, and paint one wall an accent color like SW Subdued Sienna or SW Baked Clay. Use turquoise accents, like in this rug. Southwest rug or cow print rug.

Dining chair in southwestern fabric or saddlebag color leather for the desk chair. The colors in the fabric would help you with the wall colors and accent piece colors.

For plants, think cactus and other succulents. You can find fake ones at the Dollar Store, Big Lots, Walmart, etc.

If you prefer a traditional style home office that hints of southwest, this photo shows a sage wall color, understated rug, leather office chair in saddlebag color, carved wooden floor vase filled with tall grasses. Use accessories to add pop of southwest color like turquoise or rust, and easily change out the accessories later.

Your proposed floor lamps are not in keeping with your Southwest theme. A more appropriate style would be craftsman or other straight legged pole with a lamp shade of leather, burlap, or rough linen. For a table lamp, think of a base like a painted jug.

I wouldn’t worry so much that the black computer hardware limits you. Just add interesting colors, wall art, and accessories around the room to look at.

For the metal finishes, you mention bronze and I hope you mean “oil rubbed bronze”. Black wrought iron would work, too. The wood and metal shelf needs to look rustic and sturdy to convey Southwestern, and avoid ikea and sauder brands that tip over easily.