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>

setup/migrate-room-registrations.test.ts

@@ -126,7 +126,7 @@ describe('migrate room registrations step', () => {
         chat_jid: 'dc:legacy-room',
         room_mode: 'tribunal',
         mode_source: 'inferred',
-        owner_agent_type: 'codex',
+        owner_agent_type: 'claude-code',
       },
     ]);
     expect(
@@ -141,12 +141,12 @@ describe('migrate room registrations step', () => {
       {
         chat_jid: 'dc:legacy-room',
         role: 'owner',
-        agent_type: 'codex',
+        agent_type: 'claude-code',
       },
       {
         chat_jid: 'dc:legacy-room',
         role: 'reviewer',
-        agent_type: 'claude-code',
+        agent_type: 'codex',
       },
     ]);
     expect(