### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

I Created an REST APIGatway with lambda handler using AWS CDK. when I hit the API the response header content type is always  set to "text/html"  instead of `application/json` . even if I changed the response template or added the header to lambda returned response. when I deploy the same stack on AWS account  the response header is fine and work as expected

### Expected Behavior

Response Header content-type to be `application/json`

### How are you starting LocalStack?

  `localstack start` command

### Steps To Reproduce

#### How are you starting localstack (e.g., `bin/localstack` command`)

    `localstack start` command

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

I'm using AWS CDK typescript application and deploy it using `cdklocal` command on localstack

Using CDK follow the steps:
- create  REST ApiGateway
- create Lambda function 
- integrate lambda with APIGatway

On Command line:
- deploy using `cdklocal deploy` command

Finally
- test the endpoint and check the response header content-type




### Environment

```markdown
- OS: Windows 
- LocalStack: latest
```


### Anything else?

When I deploy the same stack on AWS account everything works fine and the response header content-type is `application/json`
import base64
import json
import logging
from abc import ABC, abstractmethod
from enum import Enum
from http import HTTPStatus
from typing import Any, Dict, Union
from urllib.parse import quote_plus, unquote_plus
from flask import Response as FlaskResponse
from requests import Response
from localstack import config
from localstack.constants import APPLICATION_JSON, HEADER_CONTENT_TYPE
from localstack.services.apigateway.context import ApiInvocationContext
from localstack.services.apigateway.helpers import (
    extract_path_params,
    extract_query_string_params,
    get_event_request_context,
)
from localstack.services.awslambda import lambda_api
from localstack.utils import common
from localstack.utils.aws import aws_stack
from localstack.utils.aws.aws_responses import LambdaResponse, flask_to_requests_response
from localstack.utils.aws.templating import VelocityUtil, VtlTemplate
from localstack.utils.common import make_http_request, to_str
from localstack.utils.json import extract_jsonpath, json_safe
from localstack.utils.numbers import is_number, to_number
from localstack.utils.strings import to_bytes
LOG = logging.getLogger(__name__)
class PassthroughBehavior(Enum):