Here are some photos of it, as is.

Your best bet is to take your pictures and your dimensions to The Container Store and use their free design services for Elfa shelving/organizers. Explain what you want to store in there, and they will put together the design. Just got a flyer that they are currently having a 30% off year-end sale on all the parts/pieces. Sometimes you can also get free installation if you watch their promotions.

You don't need pull out shelves if it's designed right. Measure to see how much room you want on the side for tall items, and put shelving above that, with fully adjustable shelves from top to bottom on the other side.

@Sabrina Alfin Interiors is that an American Retailer? I'm in Canada.

Yes, but I believe Elfa is a European brand. See if they have local dealers.

Probably the easiest thing to do is to remove the old shelves and supports, and install, say, four Closet Maid (or Rubbermaid) 84" standards (with a hang track) starting at the baseboard or floor. Hang brackets (which are available up to 21.75" long) from the standards to support shelves. Shelves can be either wire (example) or solid and are available at various depths. You could run some shelves all the way across the closet, or use shorter shelves arranged into columns; Home Depot will cut long shelves to whatever length you want. You could hang mops and brooms from the shelves using hooks, and place totes or other containers on the shelves. Closet Maid and Rubbermaid components are largely interchangeable: I used Closet Maid brackets and wire shelves with Rubbermaid brackets and solid shelves.

I would be inclined to put shallow shelves on one end or the other, and leave the other end open for taller storage. If you want pullouts consider the ikea pax. It’s a great closet organization system—most organizers are about 15 inches, but there is a pax 22 3/4 depth option that might just fit for you and maximize all your space. It’s advertised for clothing storage, but photos abound of all sorts of other uses. I have both the 14 and 22 inch deep options myself, and think both are great.

Consider using the vertical drawers idea: Create a pair of storage units that fit in the center of the closet but roll out -- one with shelving for kitchen pantry items and one with both shelf and hanging for mops and brooms ( hanging over your mop bucket for cleaning items.

Creating individual roll out storage for two different types of items for which you need storage space could keep those kinds of items separate but in the same closet -- and do so while eliminating the need to physically step into the closet to get the items on either of those rolling units -- thus, leaving more room for you to include any built in items you want on each side/end of the closet -- items that you can more easily reach with the two rolling units are out of the closet.

You could create just one roll out cabinet for your cleaning items, enabling you to move your cleaning closet room to room with you for cleaning or to a garage otherwise out of the house as needed when you don't want those mop smells in the closet.