Represents a running Fact database instance and orchestrates indexing, event tracking, and record publishing.

Fact.Database is a GenServer that maintains state about:

• The database's ledger position
• Active indexers and their progress
• Locks for safe concurrent access
• The last published position to subscribers

This module provides:

• Reading events, indexes, and the ledger
• Ensuring and starting indexers
• Tracking indexer progress and publishing indexed positions
• High-level coordination of database internals via Fact.Registry and Fact.EventPublisher