Could you put risers underneath the legs of your bed so the bedskirt drapes correctly? Seems to me the boxspring to closer to the floor than it is in the picture.

5" Black Bed Risers, For Furniture, Beds, Tables, Chairs, Sofas, Set of 4 · More Info

You may still have to press the bedskirt for the crisp look you're going for.

Yes, on the risers, and get a steamer to get a pressed look.

you may even need to starch it for a crisp look.

I prefer mattress wraps, fit and neater look.

https://standardtextilehome.com/products/circa-bed-wrap?variant=18475730534513

If wanting to keep, just remove mattress and fold a seam in middle wide enough to bring up both sides to meet floor and pull up further on box spring length wise. No harm trying, as I’ve done this and it stayed in place. Trying spraying with starch and iron for a crisper look.

I have found more weighty, well made bedskirts with pleats in corners only have clean lines and be sure the dimensions reflect the appropriate distance.

They're made in 14" and 15" lengths. Maybe you bought a 15 and need a 14? If so, and you can return it, do that and look for a shorter one. If it's already the shorter size, try one of the suggested fixes.

I have used an iron on interfacing that I cut to fit the inside of the ruffle and then press on....use very light heated iron.....interfacing can melt! It makes the dust ruffle opaque and gives it some weight. You seem to have microfiber skirt and it is very soft fabric....cotton or linen will have a heavier weight and hang better, but you still might have to line it.