fix: re-derive conversation authorship from history

Rooms that Reddit returns without timeline events in /sync fell back to
isFromUs=false, so an unanswered opener of ours was projected as inbound
and surfaced in the dashboard's "Needs reply" queue. loadDetails already
paginates the authoritative history for lastMessageSnippet/Time, so take
isFromUs from the same newest message.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

src/services/chat/service.ts

@@ -1135,8 +1135,14 @@ export class ChatService {
       return;
     }
 
-    chat.lastMessageSnippet = chat.messages[chat.messages.length - 1].text;
-    chat.lastMessageTime = chat.messages[chat.messages.length - 1].timestamp;
+    const newest = chat.messages[chat.messages.length - 1];
+    chat.lastMessageSnippet = newest.text;
+    chat.lastMessageTime = newest.timestamp;
+    // Re-derive authorship from the authoritative history. Room summaries built
+    // from /sync default `isFromUs` to false when the room carries no timeline
+    // events (Reddit omits them for idle rooms), which would otherwise leave an
+    // unanswered opener of ours sitting in the operator's "Needs reply" queue.
+    chat.isFromUs = newest.isSelf;
 
     const firstSelf = chat.messages.find((m) => m.isSelf);
     if (firstSelf) chat.originMessage = firstSelf.text;