Add structured logging and centralized error handling

- Initialize slog in the serve command with terminal/file support
- Introduce `AppError` with HTTP status for unified service-layer errors
- Replace ad-hoc `api.Error` calls with `api.RespondError`
- Wrap internal errors with `model.NewInternalError` and add reference
  IDs
- Add `RequestID` middleware and switch router from `gin.Default` to
  `gin.New`

internal/api/response.go

@@ -1,7 +1,16 @@
 package api
 
 import (
+	"crypto/rand"
+	"encoding/hex"
+	"errors"
+	"fmt"
+	"log/slog"
+	"net/http"
+
 	"github.com/gin-gonic/gin"
+
+	"github.com/dhao2001/mygo/internal/model"
 )
 
 // ErrorResponse is the standard JSON body for HTTP API errors.
@@ -22,3 +31,42 @@ func Error(c *gin.Context, status int, message string) {
 		},
 	})
 }
+
+// RespondError unpacks an error from the service layer and writes a JSON
+// error response. It expects *model.AppError; unexpected non-AppError
+// values are treated as 500 with a safe message. For 500+ errors, a
+// random reference hash is included in the response so operators can
+// correlate it with server logs.
+func RespondError(c *gin.Context, err error) {
+	var ae *model.AppError
+	if !errors.As(err, &ae) {
+		ref := randomHex(8)
+		slog.ErrorContext(c.Request.Context(), "non-AppError escaped to handler",
+			"ref", ref, "error", err, "type", fmt.Sprintf("%T", err))
+		Error(c, http.StatusInternalServerError, "internal server error (ref: "+ref+")")
+		return
+	}
+
+	// 500+ errors: log full detail with a reference hash, return sanitized message.
+	if ae.Status >= 500 {
+		ref := randomHex(8)
+		slog.ErrorContext(c.Request.Context(), "internal server error",
+			"ref", ref, slog.Any("error", ae.Err), "message", ae.Message)
+		Error(c, ae.Status, "internal server error (ref: "+ref+")")
+		return
+	}
+
+	// 4xx errors with internal cause: log at WARN for diagnostics.
+	if ae.Err != nil {
+		slog.WarnContext(c.Request.Context(), ae.Message,
+			"status", ae.Status, slog.Any("error", ae.Err))
+	}
+
+	Error(c, ae.Status, ae.Message)
+}
+
+func randomHex(n int) string {
+	b := make([]byte, n)
+	rand.Read(b)
+	return hex.EncodeToString(b)
+}