### Check for existing issues

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

### What happened?

A bug happened!When creating a Virtual Key restricted to specific models (e.g., only allowed to use Sonnet 4.5), navigating to the Playground and authenticating with that Virtual Key still displays all proxy-configured models in the model selection dropdown.

The dropdown should restrict visibility and only display the specific models that the authenticated Virtual Key has explicit permission to use.

### Steps to Reproduce

Go to the LiteLLM Admin UI -> Virtual Keys section.

Generate a new key and restrict it to a single model (e.g., Sonnet 4.5).

Navigate to the Playground tab.

Set up/authenticate the playground using the newly created restricted Virtual Key.

Click on the Select Model dropdown list.

### Relevant log output

```shell

```

### What part of LiteLLM is this about?

UI Dashboard

### What LiteLLM version are you on ?

v1.88.5

### Twitter / LinkedIn details

_No response_