Optimize stale todo resolution performance

Goal

Optimize for high-scale deployments. Add database index and performance monitoring.

🎯 Optional but recommended for GitLab.com scale

Related to #20637 (closed)

Can be done in parallel with or after Phase 1d

Implementation Details

1. Database Index Migration

Location: db/migrate/XXXXXX_add_index_for_stale_todos.rb

Add partial index for query optimization:

• Columns: [:target_type, :target_id, :state, :action]
• WHERE clause: state = 'pending' AND target_type = 'MergeRequest'
• Use add_concurrent_index for zero-downtime

2. Performance Instrumentation

Add logging for large batch resolutions and Prometheus metrics.

Test Coverage Required

• Migration tests
• Performance benchmarks (100+ todos)
• Verify index is used in query plans

Files to Create

• db/migrate/XXXXXX_add_index_for_stale_todos.rb
• spec/migrations/XXXXXX_add_index_for_stale_todos_spec.rb
• Update app/services/todo_service.rb with instrumentation

Acceptance Criteria

• Index created successfully
• Migration uses concurrent index
• Query performance improves
• Database review approved

Expected Improvements

• Query time: 50-100ms → <10ms
• Consistent performance regardless of table size

Estimated Effort: 2-3 days