Background

Part of #363 — Phase 5

Refactor database_coordinator to use service_container for backend resolution.

Current State

database_system uses a lifecycle-driven database_coordinator pattern with adapter/backend layers.
Has service_registration.h for IDatabase but coordinator manages its own initialization order.

Scope

• Refactor database_coordinator to register adapters via service_container
• Leverage service_container's lazy singleton for dependency ordering
• Update adapter initialization patterns
• Verify all database_system tests pass

Key Challenges

• Phase-aware initialization (Logger → Monitor → Thread) must be preserved
• Multiple backends per adapter (runtime selection via enum factory)
• Aggregated health checks across adapters

Affected Files

• database/integrated/core/database_coordinator.h (refactor)
• database/integrated/adapters/ (update registration)
• include/kcenon/database/di/service_registration.h (extend)

Acceptance Criteria

• Adapters registered through service_container
• Initialization ordering preserved
• All tests pass under ASAN and TSAN
• Migration guide documented