If you can find a couple of Ikea cabinet bases that m/l match the existing cabinets, you could use pull-outs--one for trash/recycling, and the other to store pet food, then keep the pet bowls in the L section.

Ikea bases.

I agree with MamaGoose, try filling it in with cabinets b/w the wall and pantry (?) cabinet.

Since you're handy, you might try putting a corner susan in the corner and cabinets on each side -- but it depends on how much space is there as to whether it would be worth it.

Do you have another place for the pet dishes? If not, then I'd forego the corner susan and stick with cabinets b/w the pantry cabinet and wall. Then, as MamaGoose suggested, the pet dishes can go under the short counter run. You'll probably have to move the dishes to access the cabinets in the corner, but if you store seldom-used items in that cabinet, I don't think it will be an issue.

I'd put a drawer base next to the pantry cabinet and then a regular base in the corner. The corner cabinet could have a drawer(s) on the bottom half, but not the top half since you wouldn't be able to access drawers in the top half b/c of the "L" counter over it.

Do you have an IKEA near you? They're well regarded, inexpensive, and will probably be very easy for you to assemble.

I used a combination of refinished cabinets, shelves and curtain cabinets for my basement kitchenette. I made shelves for the corner to unite the cabinets:

https://www.houzz.com/photos/my-pics-work-in-progress-phvw-vp~65270573

This kitchen used a combination of cabinets, shelves with crates and a curtain: