### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

When a user is created, an invitation email will not be sent.

Email notifications are set up as described in the documentation (https://docs.litellm.ai/docs/proxy/email#usage). No custom email branding has been configured.

It does not seem to be a duplicate of #19860 because no email branding is applied here.

Please also note that other email notifications, such as those relating to getting started or key creation, are still being sent without any problems.

### Steps to Reproduce

1. Config File: ```yaml litellm_settings: callbacks: ["smtp_email"] ``` 2. Create new User

### Relevant log output

```shell LiteLLM Proxy:WARNING: user_management_event_hooks.py:118 - Defaulting to using Legacy Email Hooks.Missing litellm-enterprise package. Please install it to use this feature. Run `pip install litellm-enterprise` ```

### What part of LiteLLM is this about?

Proxy

### What LiteLLM version are you on ?

v1.81.0

### Twitter / LinkedIn details

_No response_