Fix owner context loss after finalize; green the test suite

Owner continuity:
- Seed a freshly created owner task with the previous task's latest owner
  final on a cold start after the previous task already closed, so a user
  reply to a finalized TASK_DONE no longer produces a "no context" answer.
  Activated for this deployment via PAIRED_CARRY_FORWARD_LATEST_OWNER_FINAL
  (.env); carried text is injected as clearly-marked background only.
- Skip intermediate STEP_DONE outputs when picking the carry-forward anchor.

Single-mode routing:
- enforceRoomModeOnLease strips a stale reviewer/arbiter lease from a room
  switched back to single, preventing single-mode messages from stalling in
  the paired path on a stuck execution lease.

Session auth / credentials:
- Pre-sync Claude credentials into each session dir before the agent spawns.
- Honor CLAUDE_CREDENTIALS_PATH in setup/login.ts (per-service isolation).
- Add a relogin-required gate so a permanently logged-out claude-code room
  asks the user to re-login instead of spawning a doomed agent.

Other:
- Arbiter verdicts written in the user's language (verdict keyword stays EN).
- status-dashboard chatName field; runtime-inventory credential path resolver.

Tests (make suite fully green: 1595 pass / 3 skip):
- service-routing: default owner is now the claude service and reviewer is
  codex-review; update the 7 failover/default expectations accordingly.
- migrate-room-registrations: owner inferred as claude-code (configured
  OWNER_AGENT_TYPE) for a dual legacy room; reviewer becomes codex.
- register: mock paired-workspace provisioning + reload signal (registration
  now provisions a workspace and hot-reloads); assert RELOADED status.
- paired-execution-context: force a claude-code reviewer to exercise the
  Claude read-only branch regardless of the deployment default.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

src/paired-execution-context.ts

@@ -229,14 +229,22 @@ function cancelOutstandingFinalizeOwnerTurn(task: PairedTask): void {
   );
 }
 
-function getLatestTurnOutputByRole(
-  taskId: string,
-  role: PairedRoomRole,
-): PairedTurnOutput | null {
+function isIntermediateStepOutput(outputText: string): boolean {
+  // STEP_DONE marks an intermediate step that keeps the task active; it is not
+  // the user-facing finalize summary, so it is a poor carry-forward anchor.
+  return /^\s*STEP_DONE\b/.test(outputText);
+}
+
+function getLatestOwnerFinalOutput(taskId: string): PairedTurnOutput | null {
+  const ownerOutputs = [...getPairedTurnOutputs(taskId)]
+    .reverse()
+    .filter((output) => output.role === 'owner');
   return (
-    [...getPairedTurnOutputs(taskId)]
-      .reverse()
-      .find((output) => output.role === role) ?? null
+    ownerOutputs.find(
+      (output) => !isIntermediateStepOutput(output.output_text),
+    ) ??
+    ownerOutputs[0] ??
+    null
   );
 }
 
@@ -248,10 +256,7 @@ function carryForwardLatestOwnerFinal(args: {
     return;
   }
 
-  const latestOwnerFinal = getLatestTurnOutputByRole(
-    args.sourceTask.id,
-    'owner',
-  );
+  const latestOwnerFinal = getLatestOwnerFinalOutput(args.sourceTask.id);
   if (!latestOwnerFinal) {
     return;
   }
@@ -293,16 +298,27 @@ export function resolveOwnerTaskForHumanMessage(args: {
     args.existingTask ?? getLatestOpenPairedTaskForChat(args.chatJid) ?? null;
 
   if (!existing) {
-    maybeRecordTaskDoneReopen(getLatestPairedTaskForChat(args.chatJid) ?? null);
+    const previousTask = getLatestPairedTaskForChat(args.chatJid) ?? null;
+    maybeRecordTaskDoneReopen(previousTask);
+    const newTask = canonicalWorkDir
+      ? createActiveTaskForRoom({
+          group: args.group,
+          chatJid: args.chatJid,
+          canonicalWorkDir,
+          roomRoleContext: args.roomRoleContext,
+        })
+      : null;
+    // Cold start after the previous task already closed (completed): seed the
+    // fresh task with the previous task's latest owner final so the owner keeps
+    // continuity across sessions instead of answering with "no context".
+    if (newTask && previousTask) {
+      carryForwardLatestOwnerFinal({
+        sourceTask: previousTask,
+        targetTask: newTask,
+      });
+    }
     return {
-      task: canonicalWorkDir
-        ? createActiveTaskForRoom({
-            group: args.group,
-            chatJid: args.chatJid,
-            canonicalWorkDir,
-            roomRoleContext: args.roomRoleContext,
-          })
-        : null,
+      task: newTask,
       supersededTask: null,
     };
   }