### 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.apigateway.context import ApiInvocationContext
from localstack.services.apigateway.helpers import (
    API_REGIONS,
    PATH_REGEX_AUTHORIZERS,
    PATH_REGEX_CLIENT_CERTS,
    PATH_REGEX_DOC_PARTS,
    PATH_REGEX_PATH_MAPPINGS,
    PATH_REGEX_RESPONSES,
    PATH_REGEX_TEST_INVOKE_API,
    PATH_REGEX_VALIDATORS,
    extract_path_params,
    extract_query_string_params,
    get_cors_response,
    get_resource_for_path,
    handle_accounts,
    handle_authorizers,
    handle_base_path_mappings,
    handle_client_certificates,
    handle_documentation_parts,
    handle_gateway_responses,
    handle_validators,
    handle_vpc_links,
    make_error_response,
)
from localstack.services.apigateway.integration import (
    RequestTemplates,
    ResponseTemplates,
    SnsIntegration,
    VtlTemplate,
)