fix: propagate log db (#17953)

It restores the TRACE logs in the DB and `/feedback`
Fix https://github.com/openai/codex/pull/16184 

Result:
https://openai.sentry.io/issues/6972946529/?project=4510195390611458&query=019d91e9-f931-7451-8852-c5240514a419&referrer=issue-stream

codex-rs/app-server/src/in_process.rs

@@ -82,6 +82,7 @@ use codex_exec_server::EnvironmentManager;
 use codex_feedback::CodexFeedback;
 use codex_login::AuthManager;
 use codex_protocol::protocol::SessionSource;
+pub use codex_state::log_db::LogDbLayer;
 use tokio::sync::mpsc;
 use tokio::sync::oneshot;
 use tokio::time::timeout;
@@ -117,6 +118,8 @@ pub struct InProcessStartArgs {
     pub cloud_requirements: CloudRequirementsLoader,
     /// Feedback sink used by app-server/core telemetry and logs.
     pub feedback: CodexFeedback,
+    /// SQLite tracing layer used to flush recently emitted logs before feedback upload.
+    pub log_db: Option<LogDbLayer>,
     /// Environment manager used by core execution and filesystem operations.
     pub environment_manager: Arc<EnvironmentManager>,
     /// Startup warnings emitted after initialize succeeds.
@@ -395,7 +398,7 @@ fn start_uninitialized(args: InProcessStartArgs) -> InProcessClientHandle {
                 loader_overrides: args.loader_overrides,
                 cloud_requirements: args.cloud_requirements,
                 feedback: args.feedback,
-                log_db: None,
+                log_db: args.log_db,
                 config_warnings: args.config_warnings,
                 session_source: args.session_source,
                 auth_manager,
@@ -728,6 +731,7 @@ mod tests {
             loader_overrides: LoaderOverrides::default(),
             cloud_requirements: CloudRequirementsLoader::default(),
             feedback: CodexFeedback::new(),
+            log_db: None,
             environment_manager: Arc::new(EnvironmentManager::new(/*exec_server_url*/ None)),
             config_warnings: Vec::new(),
             session_source,