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/model/log.rs

@@ -0,0 +1,14 @@
+use serde::Serialize;
+
+#[derive(Clone, Debug, Serialize)]
+pub struct LogEntry {
+    pub ts: i64,
+    pub ts_nanos: i64,
+    pub level: String,
+    pub target: String,
+    pub message: Option<String>,
+    pub fields_json: String,
+    pub module_path: Option<String>,
+    pub file: Option<String>,
+    pub line: Option<i64>,
+}