### 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
invocation_context: ApiInvocationContext,
) -> ApiInvocationContext:
    
    values = (
        invocation_context.api_id,
        invocation_context.stage,
        invocation_context.path_with_query_string,
    )
    if all(values):
        return invocation_context
    
    if invocation_context.is_websocket_request():
        return invocation_context
    path = invocation_context.path
    headers = invocation_context.headers
    path_match = re.search(PATH_REGEX_USER_REQUEST, path)
    host_header = headers.get(HEADER_LOCALSTACK_EDGE_URL, "") or headers.get("Host") or ""
    host_match = re.search(HOST_REGEX_EXECUTE_API, host_header)
    test_invoke_match = re.search(PATH_REGEX_TEST_INVOKE_API, path)
    if path_match:
        api_id = path_match.group(1)
        stage = path_match.group(2)
        relative_path_w_query_params = "/%s" % path_match.group(3)
    elif host_match:
        api_id = extract_api_id_from_hostname_in_url(host_header)
        stage = path.strip("/").split("/")[0]