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/migrations/0002_logs.sql

@@ -0,0 +1,14 @@
+CREATE TABLE logs (
+    id INTEGER PRIMARY KEY AUTOINCREMENT,
+    ts INTEGER NOT NULL,
+    ts_nanos INTEGER NOT NULL,
+    level TEXT NOT NULL,
+    target TEXT NOT NULL,
+    message TEXT,
+    fields_json TEXT NOT NULL,
+    module_path TEXT,
+    file TEXT,
+    line INTEGER
+);
+
+CREATE INDEX idx_logs_ts ON logs(ts DESC, ts_nanos DESC, id DESC);