### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

We are using the `Authorization` header for routing purposes

```
 "authorization: AWS4-HMAC-SHA256 <...>"
```

https://github.com/localstack/localstack/issues/5770

### Expected Behavior

Use a custom header to avoid causing confusion with backend integrations

### How are you starting LocalStack?

With a `docker run` command

### Steps To Reproduce

Run a custom HTTP integration without authorisation

### Environment

```markdown
- OS: 
- LocalStack:
```


### Anything else?

No
from localstack.services.awslambda import lambda_api
from localstack.services.generic_proxy import ProxyListener
from localstack.services.kinesis import kinesis_listener
from localstack.services.stepfunctions.stepfunctions_utils import await_sfn_execution_result
from localstack.utils import common
from localstack.utils.analytics import event_publisher
from localstack.utils.aws import aws_responses, aws_stack
from localstack.utils.aws.aws_responses import (
    LambdaResponse,
    flask_to_requests_response,
    request_response_stream,
    requests_response,
)
from localstack.utils.aws.request_context import MARKER_APIGW_REQUEST_REGION, THREAD_LOCAL
from localstack.utils.common import camel_to_snake_case, json_safe, long_uid, to_bytes, to_str
from localstack.utils.http import add_query_params_to_url
LOG = logging.getLogger(__name__)
TARGET_REGEX_PATH_S3_URI = (
    r"^arn:aws:apigateway:[a-zA-Z0-9\-]+:s3:path/(?P<bucket>[^/]+)/(?P<object>.+)$"
)
TARGET_REGEX_ACTION_S3_URI = r"^arn:aws:apigateway:[a-zA-Z0-9\-]+:s3:action/(?:GetObject&Bucket\=(?P<bucket>[^&]+)&Key\=(?P<object>.+))$"
PATH_REGEX_USER_REQUEST = (
    r"^/restapis/([A-Za-z0-9_\\-]+)(?:/([A-Za-z0-9\_($|%%24)\\-]+))?/%s/(.*)$" % PATH_USER_REQUEST
)
HOST_REGEX_EXECUTE_API = (
    r"(?:.*://)?([a-zA-Z0-9-]+)\.execute-api\.(%s|([^\.]+)\.amazonaws\.com)(.*)"
    % LOCALHOST_HOSTNAME
)
REQUEST_TIME_DATE_FORMAT = "%d/%b/%Y:%H:%M:%S %z"
class AuthorizationError(Exception):