There are many duplicate definitions because each method has its own ID and definitions.

[
  {
    "$id": "...",
    "definitions": { ... } // duplicate definitions
  },
  {
    "$id": "...",
    "definitions": { ... } // duplicate definitions
  }
]

The "Cat" and "Dog" definitions are missing the species property, which is causing Autocomplete to fail.

Use a root object with "$defs/methods" and "$defs/models" to put all methods and structs a single time.
    It's worth noting that "definitions" is deprecated, as mentioned in the JSON Schema draft specification. https://json-schema.org/draft/2020-12/draft-bhutton-json-schema-00#rfc.appendix.G

{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "$id": "...",
  "title": "...",

  "$defs": {
    "methods": {
      "processAnimal": {
        "$id": "com.linecorp.armeria.server.docs.PolymorphismDocServiceTest$AnimalService/processAnimal/POST",
        "title": "processAnimal",
        "type": "object",
        "properties": {
          "animal": {
            "$ref": "#/$defs/models/Animal" 
          }
        },
        "required": [ "animal" ]
      },
      "processZoo": {
        ...
      }
    },

    "models": {
      "Animal": {
        "type": "object",
        "oneOf": [
          { "$ref": "#/$defs/models/Dog" },
          { "$ref": "#/$defs/models/Cat" }
        ],
        "discriminator": {
          "propertyName": "species",
          "mapping": {
            "dog": "#/$defs/models/Dog",
            "cat": "#/$defs/models/Cat"
          }
        }
      },
      "Cat": {
        "type": "object",
        "properties": {
          "species": { "type": "string" },
          "name": { "type": "string" },
          "likesTuna": { "type": "boolean" },
          "scratchPost": { "$ref": "#/$defs/models/Toy" },
          "vetRecord": { "$ref": "#/$defs/models/VetRecord" }
        },
        "required": [ "name", "likesTuna", "scratchPost", "vetRecord" ]
      },
      "Dog": {
        ...
      },
      ...
    }
  }
}

Update RequestBody.tsx to align with the new schema format. (I might help you if you are not familiar with the frontend)