feat(kanban): auto-resolve merge-all conflicts with an agent

When the merge-all batch hits a conflict, spawn a conflict-resolution
agent in the main worktree (where the merge is mid-conflict), await it,
and continue the batch through the remaining branches instead of
aborting for manual resolution.

- worktrees: replace abort-on-conflict mergeBranches with non-aborting
  attemptMerge (leaves the tree mid-merge, returns conflicted paths),
  plus abortMerge/hasMergeInProgress/unmergedPaths/createRecoveryBranch.
  Batch types gain conflict/resolutionRunId/recoveryRef.
- prompt: buildConflictResolutionPrompt resolves both sides preserving
  intent, honors repo conventions (no Rust warning suppression), runs
  cargo/pnpm checks, then completes the merge with a commit.
- runs: mergeAll() is async; per branch it attemptMerges, and on conflict
  starts a streamable resolution run in REPO_ROOT, awaits it, and
  verifies the merge actually completed (no MERGE_HEAD, clean tree) before
  continuing — otherwise aborts and halts. A mergeBatchInProgress guard
  prevents two batches at once; a pre-batch recovery ref snapshots HEAD.
- route: /runs/merge-all is async; node request/socket timeouts disabled
  so a long multi-conflict batch survives.
- UI: per-branch status shows "conflict resolved by agent" + resolution
  run id; a recovery-ref banner documents how to roll the batch back.

Safety: resolution only counts if verified; otherwise the merge is
aborted and main left clean. Resolution runs are real agent_runs (stream
into the dock, stoppable) and own no worktree.
EOF && echo "" && git log --oneline -3

apps/api/src/routes/orchestrator.ts

@@ -144,8 +144,18 @@ orchestrator.post('/runs/:id/merge', (c) => {
   return c.json(mergeBranch(run.branch));
 });
 
-/** Merge all reviewable agent branches into the main branch sequentially. */
-orchestrator.post('/runs/merge-all', (c) => c.json(runManager.mergeAll()));
+/** Merge all reviewable agent branches into the main branch sequentially,
+ * spawning a conflict-resolution agent on any conflict. May block for a long
+ * time while agents resolve conflicts. */
+orchestrator.post('/runs/merge-all', async (c) => {
+  try {
+    const result = await runManager.mergeAll();
+    return c.json(result);
+  } catch (err) {
+    const message = err instanceof Error ? err.message : 'merge-all failed';
+    return c.json({ error: message }, 409);
+  }
+});
 
 /** Whether a Bevy playtest is running for a run. */
 orchestrator.get('/runs/:id/bevy', (c) => {