### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

localstack v0.12.17 released with this enhancement that downcases all headers:

> canonicalize HTTP header names in API GW Lambda events to lower-case
> https://github.com/localstack/localstack/commit/657d9fe4bd0e3c4284e6fa67aec62d265d5d9fff

This does not match what we observe in production - custom headers are not downcased. See this part of the docs on API Gateway and how it canonicalizes headers:

> API Gateway enacts the following restrictions and limitations when handling methods with either Lambda integration or HTTP integration.
> * Header names and query parameters are processed in a case-sensitive way.
> * The following table lists the headers that may be dropped, remapped, or otherwise modified when sent to your integration endpoint or sent back by your integration endpoint. In this table: 
> https://docs.aws.amazon.com/apigateway/latest/developerguide/api-gateway-known-issues.html

### Expected Behavior

I would expect that localstack follows the same canonicalization rules that API Gateway implements.

### 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`)

    docker run localstack/localstack:0.12.17

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

Used [Insomnia](https://insomnia.rest/) client to issue a POST request to an AWS Lambda function via API Gateway with custom headers. For example, `X-A-Custom-Header`. Attempt to read the custom header in your lambda function case sensitively.


### Environment

```markdown
- OS: macOS for POST request + whatever the docker container uses for localstack
- LocalStack: 0.12.17
```


### Anything else?

_No response_
# This 
            apigw_client.get_integration(
                restApiId=api_id, resourceId=api_resource["id"], httpMethod="GET"
            )
        self.assertEqual(ctx.exception.response["Error"]["Code"], "NotFoundException")
        
        lambda_client = aws_stack.create_external_boto_client("lambda")
        lambda_client.delete_function(FunctionName=lambda_name)
        apigw_client.delete_rest_api(restApiId=api_id)
    def test_api_gateway_handle_domain_name(self):
        domain_name = "%s.example.com" % short_uid()
        apigw_client = aws_stack.create_external_boto_client("apigateway")
        rs = apigw_client.create_domain_name(domainName=domain_name)
        self.assertEqual(200, rs["ResponseMetadata"]["HTTPStatusCode"])
        rs = apigw_client.get_domain_name(domainName=domain_name)
        self.assertEqual(200, rs["ResponseMetadata"]["HTTPStatusCode"])
        self.assertEqual(domain_name, rs["domainName"])
        
        apigw_client.delete_domain_name(domainName=domain_name)
    def _test_api_gateway_lambda_proxy_integration_any_method(self, fn_name, path):
        self.create_lambda_function(fn_name)
        
        lambda_uri = aws_stack.lambda_function_arn(fn_name)
        target_uri = aws_stack.apigateway_invocations_arn(lambda_uri)
        result = testutil.connect_api_gateway_to_http_with_lambda_proxy(
            "test_gateway3",
            target_uri,
            methods=["ANY"],
            path=path,
            stage_name=self.TEST_STAGE_NAME,