feat: add type column to dm_messages for system message support

Adds a `type` column (TEXT NOT NULL DEFAULT 'user') to the dm_messages
table via schema, migration, and type definition. Updates
buildDmMessageWithUser and the inline replyTo builder in the GET
messages handler to include the field in all DM message responses.

packages/shared/src/types.ts

@@ -281,6 +281,7 @@ export interface DmMessage {
   dmChannelId: string;
   userId: string;
   content: string | null;
+  type?: 'user' | 'system';
   createdAt: number;
   // Compatibility fields
   channelId?: string;