### 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_
API_PATH_LAMBDA_PROXY_BACKEND_ANY_METHOD = "/lambda-any-method/foo1"
    API_PATH_LAMBDA_PROXY_BACKEND_ANY_METHOD_WITH_PATH_PARAM = "/lambda-any-method/{test_param1}"
    API_PATH_LAMBDA_PROXY_BACKEND_WITH_IS_BASE64 = "/lambda-is-base64/foo1"
    
    TEST_STREAM_KINESIS_API_GW = "test-stream-api-gw"
    TEST_STAGE_NAME = "testing"
    TEST_LAMBDA_PROXY_BACKEND = "test_lambda_apigw_backend"
    TEST_LAMBDA_PROXY_BACKEND_WITH_PATH_PARAM = "test_lambda_apigw_backend_path_param"
    TEST_LAMBDA_PROXY_BACKEND_ANY_METHOD = "test_lambda_apigw_backend_any_method"
    TEST_LAMBDA_PROXY_BACKEND_ANY_METHOD_WITH_PATH_PARAM = (
        "test_lambda_apigw_backend_any_method_path_param"
    )
    TEST_LAMBDA_PROXY_BACKEND_WITH_IS_BASE64 = "test_lambda_apigw_backend_with_is_base64"
    TEST_LAMBDA_SQS_HANDLER_NAME = "lambda_sqs_handler"
    TEST_LAMBDA_AUTHORIZER_HANDLER_NAME = "lambda_authorizer_handler"
    TEST_API_GATEWAY_ID = "fugvjdxtri"
    TEST_API_GATEWAY_AUTHORIZER = {
        "name": "test",
        "type": "TOKEN",
        "providerARNs": ["arn:aws:cognito-idp:us-east-1:123412341234:userpool/us-east-1_123412341"],
        "authType": "custom",
        "authorizerUri": "arn:aws:apigateway:us-east-1:lambda:path/2015-03-31/functions/"
        + "arn:aws:lambda:us-east-1:123456789012:function:myApiAuthorizer/invocations",
        "authorizerCredentials": "arn:aws:iam::123456789012:role/apigAwsProxyRole",
        "identitySource": "method.request.header.Authorization",
        "identityValidationExpression": ".*",
        "authorizerResultTtlInSeconds": 300,
    }
    TEST_API_GATEWAY_AUTHORIZER_OPS = [{"op": "replace", "path": "/name", "value": "test1"}]
    def test_create_rest_api_with_custom_id(self):