test(central-ui): Playwright Flow Debugger live run + localStorage restore against the rig

An ephemeral inbound method (created and deleted through the CLI, with a never-taken
Route.To branch so prediction resolves a route target) is run live in a real browser through
the fixture's /auth/login; the reload test drives the OnAfterRenderAsync localStorage restore
and then proves the page is still interactive. Both fail on the pre-fix image at the
'Predicted' wait (the circuit deadlock) and pass on the fixed one.

Claude-Session: https://claude.ai/code/session_01NcMG6xXdsJbmD2wYAgkK29

docs/plans/2026-09-06-flow-debugger-followups.md.tasks.json

@@ -74,7 +74,7 @@
     {
       "id": 9,
       "subject": "Task 9: Playwright \u2014 browser Live run + localStorage restore (rig)",
-      "status": "pending",
+      "status": "completed",
       "blockedBy": [
         8,
         4,
@@ -90,5 +90,5 @@
       ]
     }
   ],
-  "lastUpdated": "2026-09-06T16:05:00Z"
+  "lastUpdated": "2026-09-06T16:30:00Z"
 }