### 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 os
import time
from unittest.mock import patch
import pytest
from botocore.exceptions import ClientError
from localstack import config
from localstack.services.apigateway.helpers import path_based_url
from localstack.services.awslambda.lambda_api import (
    BATCH_SIZE_RANGES,
    INVALID_PARAMETER_VALUE_EXCEPTION,
)
from localstack.services.awslambda.lambda_utils import (
    LAMBDA_RUNTIME_NODEJS14X,
    LAMBDA_RUNTIME_PYTHON36,
    LAMBDA_RUNTIME_PYTHON37,
)
from localstack.utils import testutil
from localstack.utils.aws import aws_stack
from localstack.utils.common import retry, safe_requests, short_uid
from localstack.utils.strings import to_bytes
from localstack.utils.sync import poll_condition
from localstack.utils.testutil import check_expected_lambda_log_events_length, get_lambda_log_events
from .functions import lambda_integration
from .test_lambda import (
    TEST_LAMBDA_LIBS,
    TEST_LAMBDA_NODEJS_APIGW_502,