fix(auth): org-scoped team tokens and header search order

app/composables/useActiveTeam.ts

@@ -1,10 +1,13 @@
 export const useActiveTeam = () => {
   const activeTeamId = useState<string | null>('activeTeamId', () => null)
   const activeLogtoOrgId = useState<string | null>('activeLogtoOrgId', () => null)
+  const logtoOrgState = useState<string | null>('logto-org-id', () => null)
 
   const setActiveTeam = (teamId: string | null, logtoOrgId?: string | null) => {
     activeTeamId.value = teamId
-    activeLogtoOrgId.value = logtoOrgId ?? null
+    const nextOrgId = logtoOrgId ?? null
+    activeLogtoOrgId.value = nextOrgId
+    logtoOrgState.value = nextOrgId
   }
 
   return { activeTeamId, activeLogtoOrgId, setActiveTeam }