The model picker should show the provider (e.

The model picker should show the provider (e.g. create sections per provider). currently it's impossible to see which model/entry is from which provider especially if multiple provider have the same model.

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| Field | Value |
| --- | --- |
| App version | 1.1.7 |
| OS | Windows 10.0.26200 |
| Theme | GitHub |
| Path | /chat |
| Tenure | Week 6 |

Start at the model picker in the desktop app's /chat view and trace how provider and model entries are assembled. The work is done when the picker visibly groups or labels entries by provider, including cases where providers offer the same model name.

Written by the indexing model from the issue text.