### 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`
return self.value
    def params(self, name=None):
        if not name:
            return self.parameters
        for k in ["path", "querystring", "header"]:
            if val := self.parameters.get(k).get(name):
                return val
        return ""
    def __getattr__(self, name):
        return self.value.get(name)
    def __repr__(self):
        return "$input"
class ApiGatewayVtlTemplate(VtlTemplate):
    """Util class for rendering VTL templates with API Gateway specific extensions"""
    def prepare_namespace(self, variables) -> Dict[str, Any]:
        namespace = super().prepare_namespace(variables)
        if stage_var := variables.get("stage_variables") or {}:
            namespace["stageVariables"] = stage_var
        input_var = variables.get("input") or {}
        variables = {
            "input": VelocityInput(input_var.get("body"), input_var.get("params")),
            "util": VelocityUtilApiGateway(),
        }
        namespace.update(variables)
        return namespace
class Templates: