This can be unfucked, but it’s going to be a little bit of a project.
What you’re dealing with: caked-on and dried food, mold.
What you need: your kitchen sink, dish soap, scrub brushes, gloves, household bleach, sponges, a dish rack or drainer, dish towels.
Take everything out of your kitchen sink. Fill it about 2/3rds of the way with very hot water, and several generous squirts of dish soap.
Add dishes until the sink is nearly full. Let them soak for at least an hour. Then, wearing gloves and using your scrub brush and sponges, work on removing all food particles from the dishes. Drain the sink.
Refill with cold water and 12 oz of bleach for every gallon of water, same dishes. The CDC has approved and consistently recommends a “weak bleach solution” (1:10 household bleach:water) followed by thorough rinsing for disinfection of dishes, cooking implements, and food preparation surfaces. Let soak for an hour, then drain sink and rinse dishes.
Refill sink about halfway with just hot water and dish soap, same dishes. Wash dishes as usual (soap, sponge, and water), rinsing thoroughly and then putting in the dish drainer. If your dish drainer fills up, dry the dishes with a towel. THEN PUT THE FIRST LOAD OF DISHES AWAY.
Repeat these steps until all your dishes are clean.