Improve model picker UX for long provider-qualified IDs (e.g. Fireworks)

## Problem

When models come from an additional provider such as Fireworks, their canonical IDs can be long (for example, `accounts/fireworks/models/kimi-k2p7-code`). In the model picker these IDs consume most of each row, while the human-readable name and context-window metadata are aggressively truncated.

This makes nearby models difficult to distinguish: several entries appear as labels such as `GPT...` or `Ki...`, and the selected-model button also loses the identifying part of the name. The picker technically contains the models, but choosing the intended variant becomes guesswork.

### Reproduction

1. Configure ThinkRail with a provider whose model IDs include a long namespace (Fireworks in this case).
2. Open the model picker.
3. Compare similarly named models such as the GPT OSS 120B/20B or Kimi variants.

## Proposed solution

Optimize the picker for long provider-qualified IDs:

- Keep the friendly model name readable as the primary label.
- Show the provider separately (for example, a `Fireworks` badge) and abbreviate or omit the repeated `accounts/fireworks/models/` prefix in the visible row.
- Preserve the full canonical ID for search, a tooltip, copy, and the accessible name.
- Let the dropdown use more available width, or wrap the secondary line, so model variants and context sizes remain distinguishable.
- Give the selected-model button a tooltip or other way to reveal the full selected model.

The precise layout can vary by viewport; the key outcome is that users can distinguish models without losing the full underlying identifier.

## Alternatives considered

Simply widening the dropdown would help on desktop but would not fully address narrow windows or mobile layouts. Showing only the canonical ID preserves technical accuracy but keeps the repeated provider namespace visually dominant.

## Additional context

Observed on Windows with a Fireworks model catalog. The current picker shows several clipped friendly names, clipped context sizes, and the full repeated provider path competing for horizontal space in every row.

Start at the model picker and selected-model button, reproducing the issue with a Fireworks catalog and long IDs such as accounts/fireworks/models/kimi-k2p7-code. Trace how friendly names, provider IDs, context-window metadata, search, tooltips, copy, and accessible names are rendered. Done means variants remain distinguishable across narrow and wide layouts while the full canonical ID remains available.

Written by the indexing model from the issue text.