### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

When creating an API Gateway with an integration of type AWS to S3, the uri to get objects from an S3 bucket is not working, returning:

`{
    "status": 400,
    "body": "{\"Type\": \"User\", \"message\": \"Error invoking integration for API Gateway ID '3en931aay2': API Gateway AWS integration action URI \\\"arn:aws:apigateway:us-east-1:s3:action/GetObject&Bucket=saxpress-drawio=Key={item}\\\", method \\\"GET\\\" not yet implemented\", \"__type\": \"InvalidRequest\"}",
    "headers": {
        "x-amzn-errortype": "InvalidRequest",
        "Content-Type": "text/html; charset=utf-8",
        "Content-Length": "280"
    }
}`

### Expected Behavior

Retrieve S3 object.

### How are you starting LocalStack?

With a docker-compose file

### Steps To Reproduce

#### How are you starting localstack (e.g., `bin/localstack` command, arguments, or `docker-compose.yml`)

```
localstack:
    image: localstack/localstack:latest
    hostname: localstack
    environment:
      - AWS_DEFAULT_REGION=us-east-1
      - EDGE_PORT=4566
      - HOSTNAME_EXTERNAL=localstack
      - SERICES=s3,lambda,apigateway,apigatewayv2
      - DEBUG=1
    ports:
      - '4566-4583:4566-4583'
      - '8055:8080'
    volumes:
      - 'saxpress-localstack-data:/tmp/localstack'
      - '/var/run/docker.sock:/var/run/docker.sock'
      - './.localstack:/docker-entrypoint-initaws.d'
```

#### Client commands (e.g., AWS SDK code snippet, or sequence of "awslocal" commands)

```
awslocal apigateway create-rest-api --region us-east-1 --name ${API_NAME} --endpoint-url=http://localhost:4566

awslocal apigateway create-resource \
  --region ${REGION} \
  --rest-api-id ${API_ID} \
  --parent-id ${PARENT_RESOURCE_ID} \
  --path-part "{proxy+}"

awslocal apigateway put-method \
  --region ${REGION} \
  --resource-id ${RESOURCE_ID} \
  --rest-api-id ${API_ID} \
  --http-method "GET" \
  --authorization-type "NONE" \
  --request-parameters "method.request.path.proxy=true"

awslocal apigateway put-integration \
  --region ${REGION} \
  --resource-id ${RESOURCE_ID} \
  --rest-api-id ${API_ID} \
  --type "AWS" \
  --http-method "GET" \
  --uri "arn:aws:apigateway:${REGION}:s3:action/GetObject&Bucket=${BUCKET_NAME}=Key={item}" \
  --credentials "${ROLE_ARN}" \
  --integration-http-method "GET" \
  --request-parameters "integration.request.path.item=method.request.queryString.proxy,integration.request.path.object=context.requestId"

awslocal apigateway put-method-response \
  --region ${REGION} \
  --resource-id ${RESOURCE_ID} \
  --rest-api-id ${API_ID} \
  --status-code "200" \
  --http-method "GET" \
  --response-parameters "method.response.header.Content-Type=true" \
  --response-models "application/json=Empty"

awslocal apigateway put-integration-response \
  --region ${REGION} \
  --resource-id ${RESOURCE_ID} \
  --rest-api-id ${API_ID} \
  --status-code "200" \
  --http-method "GET" \
  --response-parameters "method.response.header.Content-Type=integration.response.header.Content-Type"
```

Testing the method:
```
root@localstack:/opt/code/localstack# awslocal apigateway test-invoke-method --rest-api-id ${API_ID} --resource-id ${RESOURCE_ID} --http-method GET --path-with-query-string index.html
{
    "status": 400,
    "body": "{\"Type\": \"User\", \"message\": \"Error invoking integration for API Gateway ID '3en931aay2': API Gateway AWS integration action URI \\\"arn:aws:apigateway:us-east-1:s3:action/GetObject&Bucket=saxpress-drawio=Key={item}\\\", method \\\"GET\\\" not yet implemented\", \"__type\": \"InvalidRequest\"}",
    "headers": {
        "x-amzn-errortype": "InvalidRequest",
        "Content-Type": "text/html; charset=utf-8",
        "Content-Length": "280"
    }
}
```

### Environment

```markdown
- OS: macOS Big Sur
- LocalStack: latest
```


### Anything else?

_No response_
apig.delete_authorizer(restApiId=self.TEST_API_GATEWAY_ID, authorizerId=authorizer_id)
        self.assertRaises(Exception, apig.get_authorizer, self.TEST_API_GATEWAY_ID, authorizer_id)
    def test_apigateway_with_lambda_integration(self):
        apigw_client = aws_stack.create_external_boto_client("apigateway")
        # creat
        lambda_name = "apigw-lambda-%s" % short_uid()
        self.create_lambda_function(lambda_name)
        lambda_uri = aws_stack.lambda_function_arn(lambda_name)
        target_uri = aws_stack.apigateway_invocations_arn(lambda_uri)
        # creat
        api = apigw_client.create_rest_api(name="test-api", description="")
        api_id = api["id"]
        root_res_id = apigw_client.get_resources(restApiId=api_id)["items"][0]["id"]
        api_resource = apigw_client.create_resource(
            restApiId=api_id, parentId=root_res_id, pathPart="test"
        )
        apigw_client.put_method(
            restApiId=api_id,
            resourceId=api_resource["id"],
            httpMethod="GET",
            authorizationType="NONE",
        )
        rs = apigw_client.put_integration(
            restApiId=api_id,
            resourceId=api_resource["id"],
            httpMethod="GET",
            integrationHttpMethod="POST",
            type="AWS",
            uri=target_uri,
            timeoutInMillis=3000,