Implement full E2E, integration, component, and unit tests, and resolve all leftover tmux-to-herdr issues in UI and core scripts

.agents/skills/multi-agent-mux-status/scripts/status.sh

@@ -93,7 +93,7 @@ def get_job_status(s):
 sessions_detail = []
 for s in d.get('herdr_sessions', []):
     name = s.get('name', '?')
-    server = s.get('herdr_server') or 'default'
+    server = s.get('herdr_workspace') or s.get('herdr_server') or 'default'
     jid, jstatus = get_job_status(s)
     pane = s.get('pane') or {}
     sessions_detail.append({
@@ -197,7 +197,7 @@ if not sessions:
     print("(no sessions registered)")
 for s in sessions:
     name = s.get('name', '?')
-    server = s.get('herdr_server') or 'default'
+    server = s.get('herdr_workspace') or s.get('herdr_server') or 'default'
     status = s.get('status', '?')
     herdr = 'alive' if f"{name}|{server}" in alive else 'dead'
     cmd = (s.get('pane') or {}).get('cmd', '?')