UX: Show preliminary gate results in execution completion view

[frankbria]

Problem

Gate results are only visible on the Review page after the user explicitly clicks 'Run Gates'. After task execution completes, users have no feedback on code quality — they must navigate away and manually trigger gate checks.

Impact

Errors discovered too late in the pipeline. Users complete execution feeling confident, then find failures only when triggering review, increasing rework loops.

Recommendation

1. Automatically run gates in the background after execution completion
2. Show preliminary gate summary in CompletionBanner: 'Passed: 3/4 gates. 1 failed (ruff: 2 errors)'
3. Highlight failed gates with a warning badge
4. Include 'Fix Issues' and 'View Full Report →' links

Acceptance Criteria

• Gates trigger automatically on execution completion
• Gate summary visible in completion banner (pass/fail counts)
• Failed gates highlighted distinctly
• User can drill into /review for full gate details
• Gates run non-blocking (don't delay completion banner)

Affected Components

web-ui/src/app/execution/[taskId]/page.tsx, web-ui/src/components/review/ReviewHeader.tsx

[coderabbitai]

🔗 Related PRs

#50 - feat: Implement Quality Gates Panel in Dashboard (#43) [merged]
#76 - Add dismissible warning banner to QualityGateStatus component [merged]
#303 - feat(gates): add BUILD validation gate for config errors [merged]
#378 - fix: lint gate returns SKIPPED when linter binary is missing (#372) [merged]
#386 - [Phase 2.5-F] Harden verification gates and add batch-level QA [merged]

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[traycerai]

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