fix(vscode): remove missing stale worktree entries

[marius-kilocode]

What Problem This Solves

Fixes #13826. Agent Manager could leave a stale worktree card permanently when the worktree directory had already been removed and terminal cleanup could not reach the backend.

Why This Change Was Made

Stale removal now checks whether the worktree path is missing after terminal cleanup fails. A confirmed missing path allows state cleanup to continue. Existing paths still fail closed and preserve the entry when terminal cleanup fails. Filesystem and branch deletion remain outside this action.

User Impact

Users can remove stale Agent Manager entries after external worktree deletion without editing .kilo/agent-manager.json.

Evidence

• bun run compile passed in packages/kilo-vscode/.
• 93 focused lifecycle and architecture tests passed.
• Isolated VS Code self-test created a disposable worktree, removed it externally, removed the stale entry in the UI, and verified it remained absent after reload.

[kilo-code-bot]

Code Review Summary

Status: No Issues Found | Recommendation: Merge

Files Reviewed (3 files)

• .changeset/fix-stale-worktree-removal.md
• packages/kilo-vscode/src/agent-manager/provider-lifecycle.ts
• packages/kilo-vscode/tests/unit/agent-manager-provider-lifecycle.test.ts

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