Move sqlite logs to a dedicated database (#13772)

## Summary
- move sqlite log reads and writes onto a dedicated `logs_1.sqlite`
database to reduce lock contention with the main state DB
- add a dedicated logs migrator and route `codex-state-logs` to the new
database path
- leave the old `logs` table in the existing state DB untouched for now

## Testing
- just fmt
- cargo test -p codex-state

---------

Co-authored-by: Codex <noreply@openai.com>

codex-rs/state/src/log_db.rs

@@ -1,7 +1,7 @@
 //! Tracing log export into the state SQLite database.
 //!
 //! This module provides a `tracing_subscriber::Layer` that captures events and
-//! inserts them into the `logs` table in `state.sqlite`. The writer runs in a
+//! inserts them into the dedicated `logs` SQLite database. The writer runs in a
 //! background task and batches inserts to keep logging overhead low.
 //!
 //! ## Usage