fix(vscode): show background agents collapse icon

[marius-kilocode]

What Problem This Solves

The expanded background agents panel shows an empty collapse button because chevron-up does not exist in the icon registry. The button still works, but its purpose is not visible.

Why This Change Was Made

Reuse the existing chevron-down icon and rotate it when the panel is expanded, matching the task header's existing toggle pattern. This keeps the fix local without adding a registry entry or changing panel behavior.

User Impact

The background agents toggle has a visible arrow in both states: up when expanded, down when collapsed.

Evidence

• Full extension compile, host/webview typecheck, lint, and 22 focused background-agent tests passed.
• Automated UI interaction in real isolated VS Code verified collapse, expansion, and collapse again with deterministic job fixtures. Screenshots were visually checked. No live model request was used.
• Read-only code review found no actionable issues.
• No directly matching issue was found.

Before and after

Matching captures from real isolated VS Code, with the same fixture data and expanded panel.

Before

After

Manual test

Open a session with background agents. Expand and collapse the panel with its arrow button. Confirm that the arrow remains visible and points up when expanded and down when collapsed.

[kilo-code-bot]

Code Review Summary

Status: No Issues Found | Recommendation: Merge

Files Reviewed (2 files)

• .changeset/fix-background-agents-chevron.md
• packages/kilo-vscode/webview-ui/src/components/chat/BackgroundAgents.tsx

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