### Check for existing issues

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

### The Feature

At the moment, the playground is limited to models that a user can access via their personal scope. If a user has no default model access, and only receives model access via Team membership, the playground isn't very useful. They can supply a virtual key for the playground, but the model picker will remain blank.

Instead, the playground should offer a team selector, which updates the model picker and mints an ephemeral key against the team to use for the session, instead of the default UI ephemeral key.

### Motivation, pitch

We're a university and deliver different model sets for different populations, and the teams feature is a great way to do that. However, the playground is also an excellent feature for users, so we want to retain that functionality. For the moment we can work around this issue by just providing all models to users with a $0 budget, but that will be non-viable for compliance reasons as we open up access more broadly.

### What part of LiteLLM is this about?

UI Dashboard

### LiteLLM is hiring a founding backend engineer, …