API Gateway ignores OpenAPI paths specification: 409 response becomes 500

I deployed an HTTP API through AWS SAM with Lambda integration. Most of the HTTP response status codes are working, but not 409. When my Lambda sends a response with status code: 409 the API responds with 500 to the client. No error logs are to be found in CloudWatch. The response works correctly when tested locally (sam start-api).

I exported that API's specification and added necessary path attributes such as 409 response. Then I reimported the OpenAPI specification (with Fail on warnings) with success. I redeployed the SAM template with the OpenAPI specification as well. But that didn't change the API behavior. But afterward, when I exported the specification it was again in its unchanged state. Here's my OpenAPI specification for one path:

openapi: '3.0.1'
info:
  title: 'files'
  version: '1.0'
servers:
  - url: 'https://{}.execute-api.eu-west-1.amazonaws.com/{basePath}'
    variables:
      basePath:
        default: 'dev'
paths:
  /files:
    put:
      summary: Returns Presigned URL for specified file
      responses:
        '200':
          description: OK.
          content:
            application/json:
              schema:
                type: object
                properties:
                  url:
                    type: string
                    description: s3 url
        '400':
          description: Bad request.
        '401':
          $ref: '#/components/responses/Unauthorized'
        '404':
          description: Not Found.
        '409':
          description: Conflict.
          content:
            application/json:
              schema:
                type: object
          headers:
            x-overwrite:
              schema:
                type: string
              description: Allows force overwrite of existing objects.
        '5XX':
          description: Internal server error.
      security:
        - Auth0Authorizer: []
      x-amazon-apigateway-integration:
        payloadFormatVersion: '2.0'
        type: 'aws_proxy'
        httpMethod: 'POST'
        uri: 'arn:aws:apigateway:REGION:lambda:path/2015-03-31/functions/arn:aws:lambda:REGION:ACCOUNTID:function:FUNCTION/invocations'
        connectionType: 'INTERNET'
components:
  responses:
    Unauthorized:
      description: Unauthorized. When missing JWT token in authorization header.
      content:
        application/json:
          schema:
            $ref: '#components/schemas/Error'
  schemas:
    Error:
      type: object
      properties:
        code:
          type: string
        message:
          type: string
      required:
        - code
        - message
  securitySchemes:
    Authorizer:
      type: 'oauth2'
      flows: {}
      x-amazon-apigateway-authorizer:
        identitySource: '$request.header.Authorization'
        jwtConfiguration:
          audience:
            - ''
          issuer: ''
        type: 'jwt'
x-amazon-apigateway-cors:
  allowMethods:
    - 'DELETE'
    - 'GET'
    - 'PATCH'
    - 'POST'
    - 'PUT'
  allowHeaders:
    - '*'
  maxAge: 0
  allowCredentials: false
  allowOrigins:
    - ''
    - ''
x-amazon-apigateway-importexport-version: '1.0'

After successful reimport the exported API response specification is defaulted to:

responses:
        default:
          description: 'Default response for PUT /files'

What might be causing the API to send the 500 response instead of 409? Why is API defaulting the response specification?