[FEATURE]: app: "Free" badge in model picker is limited to the opencode provider #59302

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Describe the enhancement you want to request

What: In OpenCode Desktop, the "Free" badge next to a model name in the model picker is only shown for models served by the opencode provider, even when models on other providers have zero cost.

The check is hard-coded to the provider in packages/app/src/providers/models/models.tsx:

export const isFreeModel = (model: { provider: { id: string }; cost?: { input: number } }) =>
  model.provider.id === "opencode" && (!model.cost || model.cost.input === 0)

The TUI uses a provider-agnostic check in packages/tui/src/component/model-options.tsx (cost.length > 0 && cost.every((c) => c.input === 0)), so the same model shows a "Free" tag in the terminal but no badge in Desktop.

Request: Show the "Free" badge based on cost alone (zero input cost across all cost tiers), regardless of provider, matching the TUI behavior.

Why it's useful: Users with self-hosted or free endpoints (e.g. a LiteLLM proxy in front of free/university models) configure cost.input: 0 on those models, but Desktop gives them no visual marker in the picker. Currently the only workaround is putting "Free" in the model display name, which is inconsistent with how built-in providers are labeled.

Expected result: Any model whose input cost is zero shows the same "Free" badge as OpenCode's own free models. No routing or billing behavior changes.

Environment: OpenCode Desktop 2.1.4 (desktop-ssh), server on Linux x86_64 (Debian 13).