### 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_
"result",
        "url",
        "path_with_replace",
    ],
)
class TestAPIGateway(unittest.TestCase):
    
    APIGATEWAY_DATA_INBOUND_TEMPLATE = """{
        "StreamName": "%s",
        "Records": [
            #set( $numRecords = $input.path('$.records').size() )
            #if($numRecords > 0)
            #set( $maxIndex = $numRecords - 1 )
            #foreach( $idx in [0..$maxIndex] )
            #set( $elem = $input.path("$.records[${idx}]") )
            #set( $elemJsonB64 = $util.base64Encode($elem.data) )
            {
                "Data": "$elemJsonB64",
                "PartitionKey": #if( $elem.partitionKey != '')"$elem.partitionKey"
                                #else"$elemJsonB64.length()"#end
            }#if($foreach.hasNext),#end
            #end
            #end
        ]
    }"""
    
    API_PATH_DATA_INBOUND = "/data"
    API_PATH_HTTP_BACKEND = "/hello_world"
    API_PATH_LAMBDA_PROXY_BACKEND = "/lambda/foo1"
    API_PATH_LAMBDA_PROXY_BACKEND_WITH_PATH_PARAM = "/lambda/{test_param1}"