feat: 完成AIController重建並提交修正報告

主要變更：
1. 重建 AIController.cs
   - 移除快取系統依賴
   - 簡化為直接 AI 調用
   - 保留錯誤處理機制

2. 完成前端慣用語統一
   - page.tsx 和 ClickableTextV2.tsx 術語統一
   - 所有 phrase 相關術語改為 idiom

3. 新增完整修正報告
   - 片語俚語統一為慣用語修正報告.md
   - 包含執行結果和測試驗證

系統現已完成術語統一和快取移除

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

backend/DramaLing.Api/Controllers/AIController.cs

@@ -0,0 +1,133 @@
+using Microsoft.AspNetCore.Mvc;
+using Microsoft.AspNetCore.Authorization;
+using DramaLing.Api.Models.DTOs;
+using DramaLing.Api.Services;
+using System.Diagnostics;
+
+namespace DramaLing.Api.Controllers;
+
+[ApiController]
+[Route("api/ai")]
+public class AIController : ControllerBase
+{
+    private readonly IGeminiService _geminiService;
+    private readonly ILogger<AIController> _logger;
+
+    public AIController(
+        IGeminiService geminiService,
+        ILogger<AIController> logger)
+    {
+        _geminiService = geminiService;
+        _logger = logger;
+    }
+
+    /// <summary>
+    /// 智能分析英文句子
+    /// </summary>
+    /// <param name="request">分析請求</param>
+    /// <returns>分析結果</returns>
+    [HttpPost("analyze-sentence")]
+    [AllowAnonymous]
+    public async Task<ActionResult<SentenceAnalysisResponse>> AnalyzeSentence(
+        [FromBody] SentenceAnalysisRequest request)
+    {
+        var requestId = Guid.NewGuid().ToString();
+        var stopwatch = Stopwatch.StartNew();
+
+        try
+        {
+            // For testing without auth - use dummy user ID
+            var userId = "test-user-id";
+
+            _logger.LogInformation("Processing sentence analysis request {RequestId} for user {UserId}",
+                requestId, userId);
+
+            // Input validation
+            if (!ModelState.IsValid)
+            {
+                return BadRequest(CreateErrorResponse("INVALID_INPUT", "輸入格式錯誤",
+                    ModelState.Values.SelectMany(v => v.Errors).Select(e => e.ErrorMessage).ToList(),
+                    requestId));
+            }
+
+            // 直接執行 AI 分析，不使用快取
+            var options = request.Options ?? new AnalysisOptions();
+            var analysisData = await _geminiService.AnalyzeSentenceAsync(
+                request.InputText, request.UserLevel, options);
+
+            stopwatch.Stop();
+            analysisData.Metadata.ProcessingDate = DateTime.UtcNow;
+
+            _logger.LogInformation("Sentence analysis completed for request {RequestId} in {ElapsedMs}ms",
+                requestId, stopwatch.ElapsedMilliseconds);
+
+            return Ok(new SentenceAnalysisResponse
+            {
+                Success = true,
+                ProcessingTime = stopwatch.Elapsed.TotalSeconds,
+                Data = analysisData
+            });
+        }
+        catch (ArgumentException ex)
+        {
+            _logger.LogWarning(ex, "Invalid input for request {RequestId}", requestId);
+            return BadRequest(CreateErrorResponse("INVALID_INPUT", ex.Message, null, requestId));
+        }
+        catch (InvalidOperationException ex)
+        {
+            _logger.LogError(ex, "AI service error for request {RequestId}", requestId);
+            return StatusCode(500, CreateErrorResponse("AI_SERVICE_ERROR", "AI服務暫時不可用", null, requestId));
+        }
+        catch (Exception ex)
+        {
+            _logger.LogError(ex, "Unexpected error processing request {RequestId}", requestId);
+            return StatusCode(500, CreateErrorResponse("INTERNAL_ERROR", "伺服器內部錯誤", null, requestId));
+        }
+    }
+
+    /// <summary>
+    /// 健康檢查端點
+    /// </summary>
+    [HttpGet("health")]
+    [AllowAnonymous]
+    public ActionResult GetHealth()
+    {
+        return Ok(new
+        {
+            Status = "Healthy",
+            Service = "AI Analysis Service",
+            Timestamp = DateTime.UtcNow,
+            Version = "1.0"
+        });
+    }
+
+    private ApiErrorResponse CreateErrorResponse(string code, string message, object? details, string requestId)
+    {
+        var suggestions = GetSuggestionsForError(code);
+
+        return new ApiErrorResponse
+        {
+            Success = false,
+            Error = new ApiError
+            {
+                Code = code,
+                Message = message,
+                Details = details,
+                Suggestions = suggestions
+            },
+            RequestId = requestId,
+            Timestamp = DateTime.UtcNow
+        };
+    }
+
+    private List<string> GetSuggestionsForError(string errorCode)
+    {
+        return errorCode switch
+        {
+            "INVALID_INPUT" => new List<string> { "請檢查輸入格式", "確保文本長度在限制內" },
+            "RATE_LIMIT_EXCEEDED" => new List<string> { "升級到Premium帳戶以獲得無限使用", "明天重新嘗試" },
+            "AI_SERVICE_ERROR" => new List<string> { "請稍後重試", "如果問題持續，請聯繫客服" },
+            _ => new List<string> { "請稍後重試" }
+        };
+    }
+}