Your cabinet maybe a little too narrow to get one of those sink cabinet pull out drawers. If you can fit one of those, they tend to fill it up front deck, and they let you pull out the drawer to access the storage that is deep on the floor in the back.

I have one of those, and then I have back of the door storage if you can’t find enough, and I can suggest back of the door storage at the lower level. That means that when you open the door, it’s easier to reach stuff stored away in the back on the floor. Because my stuff is in front of it; that stuff swung out along with the door

Side mount pull out drawers on the walls perhaps. I have hooks on the side walls of my bathroom sink cabinet where I hang a hand mirror, a drain clearing tool that I reuse, and maybe even a seldom-used hair dryer.

I want to do some googling on your behalf, so I’m gonna just saw this now so I don’t use it. I’ll come back and edit it later

Measure how much space you have between the drain pipe and the wall on each side, and see if you can find an “under sink organizer” that width. You might have to account for the door hinge too.

Or see if you can find a plastic shoe drawer you can stack there.

https://www.target.com/s/under+sink+storage+drawers

This one is only 6.75 inches wide. And it’s bottom drawer looks tall, which is a good thing (a lot of these won’t let you stand a bottle up in the bottom—check that before you buy). https://www.target.com/p/2-tier-slide-out-storage-rack-slim-threshold/-/A-77353860

Also 6.75”, but not as sturdy looking: https://www.target.com/p/wood-handle-tiered-slide-out-organizer-black-brightroom-8482/-/A-83368324

This one is short and might fit under the drain, and then you can stack stuff on top of it. It could hold smaller items. https://www.target.com/p/small-stackable-slide-out-drawer-brightroom/-/A-83681729

Amazon has a ton of these

https://www.amazon.com/Under-Sink-Organizers/b

8.5” wide: https://www.amazon.com/Organizer-Sliding-Cabinet-Organizers-Bathroom/dp/B09LKPRQ6Q

10.8” wide. https://www.amazon.com/DecoBros-Stackable-Cabinet-Sliding-Organizer/dp/B00KV5NRHC

These look narrow: https://www.bedbathandbeyond.com/store/product/squared-away-2-tier-mesh-storage-cabinet-w-sliding-basket-drawers/5599967

I tend to like the ones of these that have a decent club basket that operate smoothly, and the shelf above so I can stack things. Though I will say that I like the one I have right now that has a basket because things don’t fall off.

There are fancy wooden units that are designed to take advantage of the height beside the drain. Here are some examples

https://www.woodworkerexpress.com/natural-maple-l-shaped-vanity-sink-base-pullout-w-blumotion-soft-close-for-24-rev-a-shelf-441-12vsbsc-1.html

Homewerks RIPVANSHELF2 Slide Out Storage Cabinet Under Sink Organizer, 19 Inch 2 Tier, Premium Wood Finish https://www.amazon.com/dp/B08J1SJ5R5/

Here are some examples of little pull out baskets that you could mount on the side wall higher up

Under Sink Organizers and Storage 2 PCS - Pull Out Cabinet Organizer Spice Rack - Wall Mount Storage Drawers Bathroom Organization Storage Basket https://www.amazon.com/dp/B08ZKXLBFX/

https://www.lakeside.com/Home-Decor/Storage/Household/Set-of-2-Stick---Slide-Organizers//prod4120198.jmp

You could also get spice rack style baskets to go on the side wall it wouldn’t pull out. And those could also go on the inside of your doors. If you’re renting, you can hang these kinds of baskets using command hooks or even command strips to stick them directly to the sides, as long as the tabs are still sticking out and you can remove them

And there are things like this set of plastic drawers, though it would only hold small items https://www.amazon.com/Poeland-Compact-Organization-Bathroom-Countertop/dp/B08J42CPFS