core/tui: non-blocking MCP startup (#6334)

This makes MCP startup not block TUI startup. Messages sent while MCPs
are booting will be queued.


https://github.com/user-attachments/assets/96e1d234-5d8f-4932-a935-a675d35c05e0


Fixes #6317

---------

Co-authored-by: pakrym-oai <pakrym@openai.com>

codex-rs/tui/src/status_indicator_widget.rs

@@ -145,7 +145,6 @@ impl Renderable for StatusIndicatorWidget {
         let elapsed_duration = self.elapsed_duration_at(now);
         let pretty_elapsed = fmt_elapsed_compact(elapsed_duration.as_secs());
 
-        // Plain rendering: no borders or padding so the live cell is visually indistinguishable from terminal scrollback.
         let mut spans = Vec::with_capacity(5);
         spans.push(spinner(Some(self.last_resume_at)));
         spans.push(" ".into());