feat(backend): shift existing research areas display_order automatically on insert and update

- Automatically increment display_order (+1) for all existing research areas with display_order >= target order in a transaction
- Handle display_order re-ordering gracefully during update operations
- Add unit test TestResearchAreasDisplayOrderShift to verify shift behavior on create/update
- Pass all Go tests and E2E test suites cleanly

backend/internal/repository/home.go

@@ -127,19 +127,84 @@ func (r *HomeRepository) GetResearchAreas(ctx context.Context) ([]models.Researc
 }
 
 func (r *HomeRepository) CreateResearchArea(ctx context.Context, a models.ResearchArea) (int, error) {
-	res, err := r.db.ExecContext(ctx, `
+	tx, err := r.db.BeginTx(ctx, nil)
+	if err != nil {
+		return 0, fmt.Errorf("begin tx: %w", err)
+	}
+	defer tx.Rollback()
+
+	if a.DisplayOrder > 0 {
+		// Shift existing research areas with display_order >= target order by +1
+		_, err = tx.ExecContext(ctx, `
+			UPDATE research_areas
+			SET display_order = display_order + 1
+			WHERE display_order >= ?
+		`, a.DisplayOrder)
+		if err != nil {
+			return 0, fmt.Errorf("shift research areas display_order: %w", err)
+		}
+	} else {
+		var maxOrder sql.NullInt64
+		_ = tx.QueryRowContext(ctx, `SELECT MAX(display_order) FROM research_areas`).Scan(&maxOrder)
+		if maxOrder.Valid {
+			a.DisplayOrder = int(maxOrder.Int64) + 1
+		} else {
+			a.DisplayOrder = 1
+		}
+	}
+
+	res, err := tx.ExecContext(ctx, `
 		INSERT INTO research_areas (name_en, name_kr, display_order)
 		VALUES (?, ?, ?)
 	`, a.NameEn, a.NameKr, a.DisplayOrder)
 	if err != nil {
 		return 0, fmt.Errorf("insert research area: %w", err)
 	}
+
+	if err := tx.Commit(); err != nil {
+		return 0, fmt.Errorf("commit tx: %w", err)
+	}
+
 	id, err := res.LastInsertId()
 	return int(id), err
 }
 
 func (r *HomeRepository) UpdateResearchArea(ctx context.Context, id int, a models.ResearchArea) error {
-	res, err := r.db.ExecContext(ctx, `
+	tx, err := r.db.BeginTx(ctx, nil)
+	if err != nil {
+		return fmt.Errorf("begin tx: %w", err)
+	}
+	defer tx.Rollback()
+
+	var oldOrder int
+	err = tx.QueryRowContext(ctx, `SELECT display_order FROM research_areas WHERE id = ?`, id).Scan(&oldOrder)
+	if err != nil {
+		if err == sql.ErrNoRows {
+			return sql.ErrNoRows
+		}
+		return fmt.Errorf("get old display_order: %w", err)
+	}
+
+	if a.DisplayOrder > 0 && a.DisplayOrder != oldOrder {
+		if oldOrder < a.DisplayOrder {
+			_, err = tx.ExecContext(ctx, `
+				UPDATE research_areas
+				SET display_order = display_order - 1
+				WHERE display_order > ? AND display_order <= ? AND id != ?
+			`, oldOrder, a.DisplayOrder, id)
+		} else {
+			_, err = tx.ExecContext(ctx, `
+				UPDATE research_areas
+				SET display_order = display_order + 1
+				WHERE display_order >= ? AND display_order < ? AND id != ?
+			`, a.DisplayOrder, oldOrder, id)
+		}
+		if err != nil {
+			return fmt.Errorf("shift research areas display_order on update: %w", err)
+		}
+	}
+
+	res, err := tx.ExecContext(ctx, `
 		UPDATE research_areas
 		SET name_en = ?, name_kr = ?, display_order = ?
 		WHERE id = ?
@@ -151,7 +216,7 @@ func (r *HomeRepository) UpdateResearchArea(ctx context.Context, id int, a model
 	if err == nil && rows == 0 {
 		return sql.ErrNoRows
 	}
-	return err
+	return tx.Commit()
 }
 
 func (r *HomeRepository) DeleteResearchArea(ctx context.Context, id int) error {