feat: add log db (#10086)

Add a log DB. The goal is just to store our logs in a `.sqlite` DB to
make it easier to crawl them and drop the oldest ones.

codex-rs/state/src/lib.rs

@@ -5,11 +5,13 @@
 //! orchestration and rollout scanning live in `codex-core`.
 
 mod extract;
+pub mod log_db;
 mod migrations;
 mod model;
 mod paths;
 mod runtime;
 
+pub use model::LogEntry;
 /// Preferred entrypoint: owns configuration and metrics.
 pub use runtime::StateRuntime;