### 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_
adjusted = self._adjust_partition(decoded, static_partition)
                return to_bytes(adjusted)
            except UnicodeDecodeError:
                
                return source
        elif not isinstance(source, str):
            
            return source
        return self.arn_regex.sub(lambda m: self._adjust_match(m, static_partition), source)
    def _adjust_match(self, match: Match, static_partition: str = None):
        region = match.group("Region")
        partition = self._partition_lookup(region) if static_partition is None else static_partition
        service = match.group("Service")
        account_id = match.group("AccountID")
        resource_path = match.group("ResourcePath")
        return f"arn:{partition}:{service}:{region}:{account_id}:{resource_path}"
    def _partition_lookup(self, region: str):
        try:
            partition = self._get_partition_for_region(region)
        except ArnPartitionRewriteListener.InvalidRegionException:
            try:
                
                
                partition = self._get_partition_for_region(config.DEFAULT_REGION)
            except self.InvalidRegionException:
                
                partition = self._get_partition_for_region(AWS_REGION_US_EAST_1)
        return partition
    @staticmethod
    def _get_partition_for_region(region: Optional[str]) -> str: