### 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_
self._test_api_gateway_lambda_proxy_integration_any_method(
            self.TEST_LAMBDA_PROXY_BACKEND_ANY_METHOD_WITH_PATH_PARAM,
            self.API_PATH_LAMBDA_PROXY_BACKEND_ANY_METHOD_WITH_PATH_PARAM,
        )
    def test_api_gateway_authorizer_crud(self):
        apig = aws_stack.create_external_boto_client("apigateway")
        authorizer = apig.create_authorizer(
            restApiId=self.TEST_API_GATEWAY_ID, **self.TEST_API_GATEWAY_AUTHORIZER
        )
        authorizer_id = authorizer.get("id")
        create_result = apig.get_authorizer(
            restApiId=self.TEST_API_GATEWAY_ID, authorizerId=authorizer_id
        )
        # ignor
        del create_result["ResponseMetadata"]
        create_expected = clone(self.TEST_API_GATEWAY_AUTHORIZER)
        create_expected["id"] = authorizer_id
        self.assertDictEqual(create_expected, create_result)
        apig.update_authorizer(
            restApiId=self.TEST_API_GATEWAY_ID,
            authorizerId=authorizer_id,
            patchOperations=self.TEST_API_GATEWAY_AUTHORIZER_OPS,
        )
        update_result = apig.get_authorizer(
            restApiId=self.TEST_API_GATEWAY_ID, authorizerId=authorizer_id
        )
        # ignor
        del update_result["ResponseMetadata"]
        update_expected = apply_patch(create_expected, self.TEST_API_GATEWAY_AUTHORIZER_OPS)
        self.assertDictEqual(update_expected, update_result)