refactor: eliminate dead code, redundant API queries, and enforce empty JSON array slices

- Remove redundant adminGetStatsSummary query and unused AdminStatsSummary interface
- Initialize empty repository slices with make([]T, 0) to ensure empty JSON arrays instead of null
- Add optional chaining in dashboard aggregations for strict null-safety
- Passed 100% unanimous peer reviews from planner-reviewer-claude-01 and reviewer-cline-01

backend/internal/repository/home.go

@@ -29,7 +29,7 @@ func (r *HomeRepository) GetResearchProjects(ctx context.Context) ([]models.Rese
 	}
 	defer rows.Close()
 
-	var projects []models.ResearchProject
+	projects := make([]models.ResearchProject, 0)
 	for rows.Next() {
 		var p models.ResearchProject
 		var kwJSON string
@@ -115,7 +115,7 @@ func (r *HomeRepository) GetResearchAreas(ctx context.Context) ([]models.Researc
 	}
 	defer rows.Close()
 
-	var areas []models.ResearchArea
+	areas := make([]models.ResearchArea, 0)
 	for rows.Next() {
 		var a models.ResearchArea
 		if err := rows.Scan(&a.ID, &a.NameEn, &a.NameKr, &a.DisplayOrder); err != nil {