Fix PowerShell chat result flow and prompt example UX

[papanda925]

Fixes

Addresses the PowerShell/WPF behavior reported after the priority-one merge.

• Prompt example is now clearly labeled as optional.
• Selecting an example no longer overwrites the Question automatically.
• Added an explicit 質問欄へ反映 button.
• Sending no longer flashes the current question in the Answer box while waiting.
• The existing conversation remains visible during the request.
• API/worker errors no longer force-switch to the Trace tab.
• Errors stay visible in the Answer tab together with the question.
• Developer tab now receives HTTP status, elapsed time, request, and response/error body even when the API request fails.
• Worker preserves the latest request/response metadata for error reporting.
• Added WPF regression checks for prompt-example behavior and error-display behavior.
• Updated PowerShell README and getting-started documentation.

No real API key is committed and CI does not make a live paid OrcaRouter request.