fix: stage agent-resolved conflicts before checking unmerged files

[cwbcheng]

Problem

When a tracked PR has merge conflicts, the conflict-resolution agent often resolves the files in the worktree without staging them (git add). PatchDeck then checks for unresolved conflicts with git diff --name-only --diff-filter=U, which reads the index's unmerged state — not the worktree content. So fully-resolved files still show as unmerged and the run is falsely declared failed with codex left unresolved merge conflicts: <files>, then falls into the code-owner fallback path. The resolution is never committed or pushed, so GitHub keeps showing "This branch has conflicts that must be resolved" forever.

Observed in production on PR cwbcheng/OpenAgent#433: the agent reported "All merge conflicts have been resolved … nothing staged/committed", then PatchDeck logged PR work error: codex left unresolved merge conflicts: tools/novelstudio/embodied-agent-runtime-control/src/contract-shapes.mjs … and the three conflict files stayed unresolved on GitHub.

Fix

After the conflict-resolution agent completes successfully, stage everything in the worktree (git add -A) before the unmerged-index check. If the agent actually left conflict markers behind, the existing marker check (git grep for <<<<<<< etc.) still catches them and fails with the more accurate "left merge conflict markers" reason, so genuinely-broken resolutions are still escalated.

Tests

• Added regression test babysitPR commits agent-resolved conflicts even when the agent does not stage them. It simulates the agent editing the conflicted file without staging: the unmerged index check only clears after PatchDeck runs git add. Fails without the fix (run fails with "left unresolved merge conflicts").
• Verified: node --import tsx --test server/babysitter.test.ts (111 tests pass), npm run check passes.

[jeremymcs]

Rebased onto main to clear the conflict.

This branch carried four commits that main had already landed separately through #163/#164/#165, and those duplicates were the source of the conflict. The branch is now just your unique commit (stage agent-resolved conflicts before checking unmerged files) on top of current main; it cherry-picked cleanly with no content conflict.

Verified locally: npm run check, npm run test:all (789 tests), npx eslint . — all green.

Note: #167 also touches babysitter.ts. Whichever of the two merges second may need a small rebase.