feat: Indicator light for model status (API)

[eckartal]

• I have searched the existing issues

Is your feature request related to a problem? Please describe it

There is currently no easy way to tell if the selected model is up or down without attempting to use it - which can lead to unnecessary delays and frustrations.

Describe the solution

Add a green/red light indicator that shows whether the currently selected model is up or down.

Teachability, documentation, adoption, migration strategy

No response

What is the motivation / use case for changing the behavior?

This would provide a clear visual cue about the status of their selected model before attempting to use it.

[imtuyethan]

I think this is quite hard to do? @louis-jan

[0xSage]

I still think this is a good idea. Why is it hard?
We already have this feature in settings:

I think Emre just means a shorter version of this that shows up in model selector