Using $defs in API Gateway Models

I am working on an API Gateway api using the Serverless Framework. The project contains a json-schema which apparently is used to create a model in API Gateway. Recently, I started to use the $defs element in the schema (https://json-schema.org/understanding-json-schema/structuring.html#defs), which is a way to re-use definitions within the same schema (pasting my schema below). However, no my deployments are failing:

Error: CREATE_FAILED: ApiGatewayMethodV1PreviewsPostApplicationJsonModel (AWS::ApiGateway::Model) Resource handler returned message: “Invalid model specified: Validation Result: warnings : [], errors : [Invalid model schema > specified. Unsupported keyword(s): [“$defs”], Model reference must be in canonical form, Model reference must be in canonical form] (Service: ApiGateway, Status Code: 400, Request ID: 7048dc90-7bb4-4259-bed8-50d7a93963d9, Extended Request ID: null)”

This probably means that $defs is not supported in JSON schema draft 4? Any other way to avoid duplications in the schema file? Here is my schema (Typescript but you get the idea):

export const inputSchema = {
  type: 'object',
  properties: {
    body: {
      type: 'object',
      oneOf: [
        {
          properties: {
            input: { type: 'string' },
            options: { "$ref": "#/$defs/options" },
          },
          required: ['input'],
        },
        {
          properties: {
            data: { type: 'string' },
            options: { "$ref": "#/$defs/options" },
          },
          required: ['data'],
        },
      ],
    },
  },
  $defs: {
    options: {
      type: 'object',
      properties: {
        camera: { type: 'string' },
        auto_center: { type: 'boolean' },
        view_all: { type: 'boolean' },
      },
    },
  },
};