#4035: fix(tui): ensure UI updates when status changes

Add missing tui.requestRender() calls after status updates to prevent UI from becoming stale. This ensures the terminal interface reflects current connection and activity status immediately. <!-- greptile_comment --> <h2>Greptile Overview</h2> <h3>Greptile Summary</h3> This PR adds `tui.requestRender()` calls after status/loader message updates so the terminal UI reflects connection/activity status changes immediately instead of getting stale. Changes are isolated to `src/tui/tui.ts`, primarily around the status rendering pipeline (`updateBusyStatusMessage`, `setConnectionStatus`, `setActivityStatus`, and the status TTL timeout). <h3>Confidence Score: 3/5</h3> - Mostly safe, but may regress TUI performance due to extra renders on timer-driven paths. - The change is small and localized, but it adds `requestRender()` calls inside hot timer paths (waiting updates at 120ms) and duplicates render triggers across layers; without certainty about `@mariozechner/pi-tui` render semantics, there’s some risk of CPU/flicker regressions. - src/tui/tui.ts (status timers and render scheduling) <!-- greptile_other_comments_section --> _{(2/5) Greptile learns from your feedback when you react with thumbs up/down!} **Context used:** - Context from `dashboard` - CLAUDE.md ([source](https://app.greptile.com/review/custom-context?memory=fd949e91-5c3a-4ab5-90a1-cbe184fd6ce8)) - Context from `dashboard` - AGENTS.md ([source](https://app.greptile.com/review/custom-context?memory=0d0c8278-ef8e-4d6c-ab21-f5527e322f13)) <!-- /greptile_comment -->