### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

Authorization headers being sent to API gateway are received on lambdas as "empty string"

### Expected Behavior

_No response_

### How are you starting LocalStack?

With a docker-compose file

### Steps To Reproduce

Run a API Gateway with lambda integration

### Environment

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


### Anything else?

_No response_
cls_dict["_ACCOUNTS_CLS"] = cls._ACCOUNTS_CLS
            cls_dict["_ACCOUNT_BACKENDS"] = cls._ACCOUNT_BACKENDS
            cls._ACCOUNTS_CLS[account_id] = type(cls.__name__, cls.__bases__, cls_dict)
        regions = cls.regions()
        backend = regions.get(region)
        if not backend:
            if MULTI_ACCOUNTS:
                backend = cls._ACCOUNTS_CLS[account_id]()
            else:
                backend = cls()
            backend.name = region
            backend.account_id = account_id
            regions[region] = backend
        return regions[region]
    @classmethod
    def initialise(cls):
        if not hasattr(cls, "_ACCOUNT_BACKENDS"):
            cls._ACCOUNT_BACKENDS = defaultdict(lambda: dict())
        if not hasattr(cls, "_ACCOUNTS_CLS"):
            cls._ACCOUNTS_CLS = dict()
        if not hasattr(cls, "REGIONS"):
            cls.REGIONS = dict()
    @classmethod
    def regions(cls: Type[T]) -> Dict[str, T]:
        """Return a map of all regions and backend instances."""
        cls.initialise()
        account_id = cls.get_current_request_account_id()
        return cls._ACCOUNT_BACKENDS[account_id]
    @classmethod
    def get_current_request_region(cls) -> str: