feat(federation): add fire-and-forget S2S typing relay

sendTypingRelay() mirrors sendCallRelay() — direct POST to peers,
no outbox, no retry. Uses federatedId for cross-instance channel
identification. Wired into handleDmTypingStart() for typing_start
and broadcastDmMessage() for typing_stop.

packages/server/src/routes/dm.ts

@@ -30,6 +30,7 @@ import {
   getGroupDmTargetOrigins,
   isFederationRelayEnabled,
   computeFederatedId,
+  sendTypingRelay,
 } from '../utils/federationOutbox.js';
 import { getOurOrigin } from '../utils/federationAuth.js';
 import type { FederationRelayEvent } from '@backspace/shared';
@@ -191,6 +192,9 @@ export function broadcastDmMessage(dmChannelId: string, message: DmMessageWithUs
     }
   }
 
+  // Relay typing stop to remote peers (fire-and-forget)
+  sendTypingRelay(dmChannelId, 'dm_typing_stop', message.userId);
+
   for (const member of dmMembers) {
     // If this member had closed the DM, resurface it first
     if (member.closed === 1) {