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`

cmd/serve.go

@@ -3,6 +3,7 @@ package cmd
 import (
 	"context"
 	"fmt"
+	"log/slog"
 	"os"
 	"os/signal"
 	"syscall"
@@ -11,6 +12,7 @@ import (
 
 	"github.com/dhao2001/mygo/internal/app"
 	"github.com/dhao2001/mygo/internal/config"
+	mygolog "github.com/dhao2001/mygo/internal/log"
 	"github.com/dhao2001/mygo/internal/server"
 )
 
@@ -26,6 +28,11 @@ var serveCmd = &cobra.Command{
 			return fmt.Errorf("load config: %w", err)
 		}
 
+		// Set up structured logging before anything else.
+		appLogger := mygolog.NewLogger(cfg.Log)
+		slog.SetDefault(appLogger)
+		slog.Info("mygo server starting")
+
 		ctx, stop := signal.NotifyContext(context.Background(), os.Interrupt, syscall.SIGTERM)
 		defer stop()