[diagnostics] show diagnostics earlier in workflow (#13604)

<img width="591" height="243" alt="Screenshot 2026-03-05 at 10 17 06 AM"
src="https://github.com/user-attachments/assets/84a6658b-6017-4602-b1f8-2098b9b5eff9"
/>

- show feedback earlier
- preserve raw literal env vars (no trimming, sanitizing, etc.)

codex-rs/tui/src/chatwidget/snapshots/codex_tui__chatwidget__tests__feedback_upload_consent_popup.snap

@@ -8,6 +8,10 @@ expression: popup
     • codex-logs.log
     • codex-connectivity-diagnostics.txt
 
+  Connectivity diagnostics
+    - OPENAI_BASE_URL is set and may affect connectivity.
+      - OPENAI_BASE_URL = hello
+
 › 1. Yes  Share the current Codex session logs with the team for
           troubleshooting.
   2. No