fix: StagehandのWorkers AI型エラーを修正 (fix regenerated types)

[haranishi]

Stagehandのサンプルで、wrangler types後にWorkers AIの入力型とoverload解決が失敗する問題を修正します。モデルIDをリテラル型のまま渡し、そのモデルの入力型に合わせてStagehandとの互換キャストを1か所にまとめます。送信するpayloadは従来どおりです。

型定義を再生成してから型チェックするCIを追加し、古い生成済み型で問題が見えなくなることを防ぎます。

The Stagehand example fails to typecheck after regenerating Workers AI declarations. Pass the existing literal model ID to Ai.run and derive its input type from AiModels[typeof modelId]["inputs"]. Keep the Stagehand compatibility cast at the input boundary and preserve the existing request payload.

Add npm run typecheck and a pull-request workflow that runs wrangler types before checking the example.

Validation:

• Reproduced the original input-type failure with the lockfile's Wrangler 4.57.0.
• Reproduced the original overload failure with Wrangler 4.149.0.
• After the fix, npm run typecheck passed with types regenerated by both versions, and with the committed type declarations.
• Generated declarations were restored after validation; this PR does not update that snapshot.

Closes #227.

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