It would be helpful to have measurements. Hard to tell the size of space with photos.

Looks to me like you could hang brooms etc on the wall in the corner to the left of the sink, and rotate the desk so it it is on the wall opposite the sink, so it does not interfere with your access to the brooms.

How much space is between the sink and the wall? If you want one cabinet to fit that space, you might try a ready-to-assemble PANTRY TYPE cabinet. But, those start at 18" wide x 24" deep x 84" high up to 96". There are similar ready-to-assemble LINEN TYPE bath cabinets, and most resemble furniture. Many are narrower, but they also tend to be shorter and might not hold an upright vacuum well, much less a broom.

Perhaps a better alternative is to leave the space next to the sink for a trash container, and put a larger cabinet on the wall opposite the sink. Still, it would be better to choose a less deep cabinet so as to allow plenty of space in front of the sink, and a wider, but less deep, linen type could work. Just remember that tall cabinets should be attached to the wall to prevent accidental tip overs.

You might find this laundry room thread interesting, although it is older. Scroll down to the great "after" pics at the end. https://www.houzz.com/discussions/3792622/sad-ugly-laundry-room#n=243

My previous house had a combined laundry room/office. It worked quite well.