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/core/src/state_db.rs

@@ -12,6 +12,7 @@ use codex_protocol::ThreadId;
 use codex_protocol::protocol::RolloutItem;
 use codex_protocol::protocol::SessionSource;
 use codex_state::DB_METRIC_BACKFILL;
+pub use codex_state::LogEntry;
 use codex_state::STATE_DB_FILENAME;
 use codex_state::ThreadMetadataBuilder;
 use serde_json::Value;