Could you possibly stack the washer and dryer and then have some cabinetry built beside it?

I'd add a few more shelves or cabinets above and a shelf just above the washer/dryer for commonly used items. The wall opposite could have several bar/hangers of different heights for hanging clothes. They even make some fold down bars for hanging that can be out of the way when needed.

A few ideas from Pinterest.

Here is a simple update we did in our laundry room...ok, more of a laundry closet. The cabinets, baskets on top, and closet door racks provide more storage than I expected. We are planning to put in a butcher block counter for a folding station. If you do a lot of hang drying, a retractable rack like this might be useful without taking up precious storage space. Also consider how your door functions. Not knowing what the rest of your space looks like, I'm not sure what will/will not work (slider, pocket door, barn door, etc). For us, we used to have bifold doors which limited our space even more. By swapping out how the door functioned, we gained storage space. Best of luck with your project!

I would do cabinets. Unless your the type who can keep it all neat in pretty jars and bins... do a tile on the wall also. As far as hanging goes do you have another wall to work with?

Other than a countertop and cabinets, if you can reverse the door swing I'd add retractable or fold-down drying racks to the right wall and a rod on the left from front to back. If the ceiling is high enough a shelf above the door could be used for buckets and cleaning supplies.

https://polder.com/collections/laundry/products/wall-mount-accordion-dryer

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If you’re an ikea shopper, take a look at their shoe cabinets. They aren’t deep, just enough to hold a pair of shoes so they don’t protrude too much into the room, have a nice top like a counter and securely attach to the walls and come in very livable colors. I have a few in my laundry room but instead of holding shoes I keep my detergent and powders and Clorox pens and a little bin for lint and lost buttons and change. I even keep extra hangers in one. The compartments tilt open and the size just seems well suited for all kinds of cleaners...plus I’m not reaching over my head to push things out of the way to grab something and then it leaves the room above the cabinets to hang a bar to hang clothes on.

These are some good ideas, thanks for sharing!! I had no idea retractable hangers could work.