### 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`
if not isinstance(s, str):
            s = json.dumps(s)
        encoded_str = s.encode(config.DEFAULT_ENCODING)
        encoded_b64_str = base64.b64encode(encoded_str)
        return encoded_b64_str.decode(config.DEFAULT_ENCODING)
    def base64Decode(self, s):
        if not isinstance(s, str):
            s = json.dumps(s)
        return base64.b64decode(s)
    def toJson(self, obj):
        return obj and json.dumps(obj)
    def urlEncode(self, s):
        return quote_plus(s)
    def urlDecode(self, s):
        return unquote_plus(s)
    def escapeJavaScript(self, s):
        try:
            return json.dumps(json.loads(s))
        except Exception:
            primitive_types = (str, int, bool, float, type(None))
            s = s if isinstance(s, primitive_types) else str(s)
        if str(s).strip() in {"true", "false"}:
            s = bool(s)
        elif s not in [True, False] and is_number(s):
            s = to_number(s)
        return json.dumps(s)
class VelocityInput: