refactor(vscode): share webview provider shell

[marius-kilocode]

The sidebar and Agent Manager each composed nearly identical provider trees. Maintaining both copies allowed a shared chat dependency to be added to one surface while leaving the other with a blank webview.

This consolidates the common provider composition into fixed provider-shell stages at the existing surface-specific cut points. The sidebar continues to own WorkStyleProvider and LocalTabsProvider, Agent Manager continues to own WorktreeModeProvider, and DataBridge stays in each root. The fixed stages preserve provider order without introducing optional provider flags or a configurable mega-component.

Architecture guards now assert the shared shell and required surface composition directly, while the existing DataBridge reactivity guards remain unchanged.

[kilo-code-bot]

Code Review Summary

Status: No Issues Found | Recommendation: Merge

Files Reviewed (4 files)

• packages/kilo-vscode/tests/unit/agent-manager-arch.test.ts
• packages/kilo-vscode/webview-ui/agent-manager/AgentManagerApp.tsx
• packages/kilo-vscode/webview-ui/src/App.tsx
• packages/kilo-vscode/webview-ui/src/context/provider-shell.tsx

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_{Reviewed by claude-sonnet-5 · Input: 12 · Output: 4.2K · Cached: 238.5K}

_{Review guidance: REVIEW.md from base branch main}