### 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
self.context = context
        self.apigateway_client = apigateway_client
    def is_request_valid(self) -> bool:
        
        if self.context.resource is None or "resourceMethods" not in self.context.resource:
            return True
        resource_methods = self.context.resource["resourceMethods"]
        if self.context.method not in resource_methods:
            return True
        
        resource = resource_methods[self.context.method]
        if not (resource.get("requestValidatorId") or "").strip():
            return True
        
        validator = self.apigateway_client.get_request_validator(
            restApiId=self.context.api_id, requestValidatorId=resource["requestValidatorId"]
        )
        if validator is None:
            return True
        
        if self.should_validate_body(validator):
            is_body_valid = self.validate_body(resource)
            if not is_body_valid:
                return is_body_valid
        if self.should_validate_request(validator):
            is_valid_parameters = self.validate_parameters_and_headers(resource)
            if not is_valid_parameters:
                return is_valid_parameters
        return True
    def validate_body(self, resource):