feat(database): add performance indexes and materialized view for optimization

- Created multiple new indexes in the performance-indexes.sql file to enhance query performance for tasks, team members, and related tables.
- Added a materialized view for team member information in 3_views.sql to pre-calculate expensive joins, improving data retrieval efficiency.
- Introduced a function to refresh the materialized view, ensuring up-to-date information while optimizing performance.
- Implemented an optimized method in tasks-controller-v2.ts to split complex queries into focused segments, significantly improving response times and overall performance.

worklenz-backend/database/migrations/20250115000000-performance-indexes.sql

@@ -79,4 +79,57 @@ ON task_priorities(value);
 
 -- Index for team labels
 CREATE INDEX CONCURRENTLY IF NOT EXISTS idx_team_labels_team 
-ON team_labels(team_id); 
+ON team_labels(team_id);
+
+-- NEW INDEXES FOR PERFORMANCE OPTIMIZATION --
+
+-- Composite index for task main query optimization (covers most WHERE conditions)
+CREATE INDEX CONCURRENTLY IF NOT EXISTS idx_tasks_performance_main
+ON tasks(project_id, archived, parent_task_id, status_id, priority_id)
+WHERE archived = FALSE;
+
+-- Index for sorting by sort_order with project filter
+CREATE INDEX CONCURRENTLY IF NOT EXISTS idx_tasks_project_sort_order
+ON tasks(project_id, sort_order)
+WHERE archived = FALSE;
+
+-- Index for email_invitations to optimize team_member_info_view
+CREATE INDEX CONCURRENTLY IF NOT EXISTS idx_email_invitations_team_member
+ON email_invitations(team_member_id);
+
+-- Covering index for task status with category information
+CREATE INDEX CONCURRENTLY IF NOT EXISTS idx_task_statuses_covering
+ON task_statuses(id, category_id, project_id);
+
+-- Index for task aggregation queries (parent task progress calculation)
+CREATE INDEX CONCURRENTLY IF NOT EXISTS idx_tasks_parent_status_archived
+ON tasks(parent_task_id, status_id, archived)
+WHERE archived = FALSE;
+
+-- Index for project team member filtering
+CREATE INDEX CONCURRENTLY IF NOT EXISTS idx_team_members_project_lookup
+ON team_members(team_id, active, user_id)
+WHERE active = TRUE;
+
+-- Covering index for tasks with frequently accessed columns
+CREATE INDEX CONCURRENTLY IF NOT EXISTS idx_tasks_covering_main
+ON tasks(id, project_id, archived, parent_task_id, status_id, priority_id, sort_order, name)
+WHERE archived = FALSE;
+
+-- Index for task search functionality
+CREATE INDEX CONCURRENTLY IF NOT EXISTS idx_tasks_name_search
+ON tasks USING gin(to_tsvector('english', name))
+WHERE archived = FALSE;
+
+-- Index for date-based filtering (if used)
+CREATE INDEX CONCURRENTLY IF NOT EXISTS idx_tasks_dates
+ON tasks(project_id, start_date, end_date)
+WHERE archived = FALSE;
+
+-- Index for task timers with user filtering
+CREATE INDEX CONCURRENTLY IF NOT EXISTS idx_task_timers_user_task
+ON task_timers(user_id, task_id);
+
+-- Index for sys_task_status_categories lookups
+CREATE INDEX CONCURRENTLY IF NOT EXISTS idx_sys_task_status_categories_covering
+ON sys_task_status_categories(id, color_code, color_code_dark, is_done, is_doing, is_todo);