feat: add 'both' agent type for shared Claude Code + Codex channels

- AgentType now supports 'both' — runs both agents sequentially
- Each agent gets its own folder suffix (_cc / _codex) for isolated sessions
- Claude Code bot handles message storage for 'both' channels
- Responses routed through the matching bot for each agent type

src/channels/discord.ts

@@ -249,7 +249,11 @@ export class DiscordChannel implements Channel {
     if (!this.agentTypeFilter) return true;
     const group = this.opts.registeredGroups()[jid];
     if (!group) return false;
-    return (group.agentType || 'claude-code') === this.agentTypeFilter;
+    const groupType = group.agentType || 'claude-code';
+    // 'both' channels are owned by the claude-code bot (primary handler for
+    // message storage and typing). The codex bot skips them to avoid duplicates.
+    if (groupType === 'both') return this.agentTypeFilter === 'claude-code';
+    return groupType === this.agentTypeFilter;
   }
 
   async disconnect(): Promise<void> {