What types of things do you anticipate wanting/needing to store there? The size/weight of those items would inform any suggestions we might make... What is controlled by the light switch there in the corner? Overhead lights? Garbage disposal in sink? How often is it used? Is your primary concern the aesthetics of that awkward space? Functional NEED for storage? Preference for open vs enclosed storage? Regardless of the answers above, I would rule out any particleboard cabinetry solutions resting on the countertop itself. Bar counters are prone to spills that would destroy the bottom of the cabinet. Best to stick to plastic or metal (with some sort of plastic/rubber feet to avoid rust-staining countertop). The short depth and high height of the space screams "tip hazard" to me, especially given your stated desire NOT to drill into the wall (even for anti-tip strap?) as a renter. This is especially important if there are young children and/or pets in the home, or if you live somewhere prone to earthquakes. Smaller Hyllis shelf or Vesten corner shelf come to mind for cheaper solutions. An OMAR-based custom solution would be much sturdier, IMHO. Something heavy like a microwave on the bottom shelf would help stabilize. Good luck! More on reddit.com

That's most likely a 15 inch wide sektion cabinet. You need these shelves: https://www.ikea.com/us/en/p/utrusta-shelf-white-10265523/ It's most likely 14 3/4 deep and 15 in wide (measure the door width to confirm width). Edit: They also have soft closing hinges. Their closing is so satisfying. More on reddit.com

Something like KALKNÄS might work. More on reddit.com

In deep cabinets, I like back-of-door storage. It effectively takes the front 3” or so of the shelf and moves it out into the room when the door swings. It creates two “fronts,” so you can see twice as many items. And it means that the stuff in the back of the deep shelf doesn’t have to “fly over” quite as many items (because 3”-ish of that stuff is on the door) Pullout shelves are also useful. ShelvesThatSlide.com sells ones are to a custom size and has good measuring and installation instructions. More on reddit.com