Convert provider picker to a two-column popup

[jasnsy]

Summary

• replace the stacked provider/model menu with a two-column popup that keeps providers on the left and models on the right
• preserve locked-provider behavior, keep coming-soon providers visible, and show an empty state when a provider has no models
• keep the popup height stable across provider switches and update browser coverage for the new interaction

Validation

• bun fmt
• bun lint
• bun typecheck

Screenshot

[vercel]

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