### 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
if not is_api_key_valid(api_key_required, headers, invocation_context.stage):
        return make_error_response("Access denied - invalid API key", 403)
    integrations = resource.get("resourceMethods", {})
    integration = integrations.get(method, {})
    if not integration:
        
        
        integration = integrations.get("ANY", {}) or integrations.get(
            "X-AMAZON-APIGATEWAY-ANY-METHOD", {}
        )
    integration = integration.get("methodIntegration")
    if not integration:
        if method == "OPTIONS" and "Origin" in headers:
            
            return get_cors_response(headers)
        return make_error_response(
            "Unable to find integration for: %s %s (%s)" % (method, invocation_path, raw_path),
            404,
        )
    res_methods = resource.get("resourceMethods", {})
    meth_integration = res_methods.get(method, {}).get("methodIntegration", {})
    int_responses = meth_integration.get("integrationResponses", {})
    response_templates = int_responses.get("200", {}).get("responseTemplates", {})
    
    invocation_context.resource = resource
    invocation_context.resource_path = extracted_path
    invocation_context.response_templates = response_templates
    invocation_context.integration = integration
    return invoke_rest_api_integration(invocation_context)
def invoke_rest_api_integration(invocation_context: ApiInvocationContext):