### 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_
from localstack.services.apigateway.helpers import (
    TAG_KEY_CUSTOM_ID,
    connect_api_gateway_to_sqs,
    gateway_request_url,
    get_resource_for_path,
    get_rest_api_paths,
)
from localstack.services.awslambda.lambda_api import add_event_source
from localstack.services.awslambda.lambda_utils import (
    LAMBDA_RUNTIME_NODEJS12X,
    LAMBDA_RUNTIME_PYTHON36,
)
from localstack.services.generic_proxy import ProxyListener
from localstack.services.infra import start_proxy
from localstack.utils import testutil
from localstack.utils.aws import aws_stack
from localstack.utils.common import clone, get_free_tcp_port, json_safe, load_file
from localstack.utils.common import safe_requests as requests
from localstack.utils.common import select_attributes, short_uid, to_str
from .test_lambda import TEST_LAMBDA_LIBS, TEST_LAMBDA_PYTHON
THIS_FOLDER = os.path.dirname(os.path.realpath(__file__))
TEST_SWAGGER_FILE = os.path.join(THIS_FOLDER, "files", "swagger.json")
TEST_IMPORT_REST_API_FILE = os.path.join(THIS_FOLDER, "files", "pets.json")
TEST_LAMBDA_ECHO_FILE = os.path.join(THIS_FOLDER, "lambdas", "lambda_echo.py")
TEST_LAMBDA_HANDLER_JS = os.path.join(THIS_FOLDER, "lambdas", "lambda_handler.js")
ApiGatewayLambdaProxyIntegrationTestResult = namedtuple(
    "ApiGatewayLambdaProxyIntegrationTestResult",
    [
        "data",
        "resource",