What about something like this? I like the wood one because it doesn‘t look like mudroom furniture.

Look for an enclosed console that fits the space. Looks like a front entryway, so perhaps storage of shoes only, and have backpacks go somewhere else (their room maybe).

Ikea has some great shoe cabinets and there are tons of hacks online that make them terrific

Ikea shoe cabinets would work, so might an Ikea Kallax unit (with baskets or boxes if you like). You didn't give any measurements, so it's hard to recommend anything specific.

Depending on the age of your children and what will work best, take a look on line for ideas that will best suit their routine/needs. For example, a closed in cabinet is nicer visually, but will they open to store backpacks (and assume jackets).

First thing is to decide though is which section to use, given the front door’s proximity/with limited width; plan accordingly and also edit console if you want ”pretty”.

The storage area is what it is, so suggest just making it practical/easy for them and perhaps will be able to keep neat. Suggest a runner to join the two areas and it will also add a nice decorative touch.

The first picture posted by Jenspizz makes them most sense - a shallow double door closet. You can put hooks inside on the back and side walls for jackets and backpacks, hung at varying heights, and toss shoes on the bottom. All of the mess stays out of sights. The space seems perfectly sized for something like this.

You can find a better way to store items under the table.

Consider painting the wall behind the entry door and assemble a better selection of basket trays for the wall. It could use more pattern, and every room needs a little BLACK!