feat(chat): add direct Live badge and harden Live monitor backend (#138)

* feat(chat): add direct live badge to session rows

* fix(live): use session DB for conversations monitor

* docs: add chat vs live monitor direction plan

* fix(search): avoid numeric session search 500 without FTS table

packages/client/src/components/hermes/chat/SessionListItem.vue

@@ -45,6 +45,7 @@ const { t } = useI18n()
           </svg>
         </span>
         <span class="session-item-title">{{ session.title }}</span>
+        <span v-if="live" class="session-item-live-badge">{{ t('chat.liveMode') }}</span>
       </span>
       <span class="session-item-meta">
         <span v-if="session.model" class="session-item-model">{{ session.model }}</span>