chore: unify log queries (#10152)

Unify log queries to only have SQLX code in the runtime and use it for
both the log client and for tests

codex-rs/state/migrations/0003_logs_thread_id.sql

@@ -0,0 +1,3 @@
+ALTER TABLE logs ADD COLUMN thread_id TEXT;
+
+CREATE INDEX idx_logs_thread_id ON logs(thread_id);