Record sent chats in messages repo and blur gallery by default

Threads MessagesRepository through ChatService so first outgoing chat
messages are persisted for stats, and extends the repo + DB client to
support chat-room-keyed lookups. Adds tests covering the new behavior.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

src/web/routes/conversations.ts

@@ -81,7 +81,7 @@ export function createConversationsRouter(ctx: WebContext): Router {
       } | null = null;
       try {
         const sent = ctx.repos.messages.getLatestByRecipient(conversation.username);
-        if (sent) {
+        if (sent && sent.postId) {
           const url = sent.subreddit
             ? `https://www.reddit.com/r/${sent.subreddit}/comments/${sent.postId}/`
             : `https://redd.it/${sent.postId}`;