chore: gitignore installers and include pending web changes

Add installers/ to .gitignore and remove from tracking — binaries
should not be in git.

Also includes:
- Re-push Electron activities after WebSocket reconnect (sleep/wake)
- Merge activity map instead of replacing to preserve local state
- Nori mascot design plan

.gitignore

@@ -5,6 +5,7 @@ node_modules/
 # Build output
 dist/
 dist-electron/
+installers/
 packages/web/dist/
 packages/server/dist/
 packages/shared/dist/

packages/web/src/hooks/useWebSocket.ts

@@ -5,7 +5,7 @@ import { useChatStore } from '../stores/chatStore';
 import { useVoiceStore } from '../stores/voiceStore';
 import { useSocialStore } from '../stores/socialStore';
 import { useSettingsStore } from '../stores/settingsStore';
-import type { ServerEvent, ClientEvent, ActiveCallInfo } from '@backspace/shared';
+import type { ServerEvent, ClientEvent, ActiveCallInfo, Activity } from '@backspace/shared';
 import { resolveAssetUrl, normalizeUserAssets, normalizeMessageAssets } from '../utils/assetUrls';
 import { broadcastVoiceStatus, broadcastDeafenViaLiveKit } from '../utils/voice';
 import { registerSelfId } from '../utils/identity';
@@ -214,6 +214,17 @@ function handleEvent(origin: string, event: ServerEvent): void {
         useActivityStore.setState({ showActivity: event.user.showActivity });
       }
 
+      // Re-push local Electron activities after reconnect (sleep/wake, network blip, etc.)
+      // The process scanner keeps running but onActivityDetected only fires on change,
+      // so if the same app was active before and after sleep, nothing would re-push.
+      if (isHome && window.backspace?.getCurrentActivity) {
+        window.backspace.getCurrentActivity().then((activity: unknown) => {
+          if (activity) {
+            useActivityStore.getState().pushActivities([activity as Activity]);
+          }
+        }).catch(() => {});
+      }
+
       // Populate voice user statuses (mute/deafen/camera/screenshare) from server
       if (event.voiceUserStates) {
         for (const [uid, status] of Object.entries(event.voiceUserStates)) {

packages/web/src/stores/activityStore.ts

@@ -41,13 +41,17 @@ export const useActivityStore = create<ActivityState>((set, get) => ({
   },
 
   initActivities: (activityMap) => {
-    const next = new Map<string, Activity[]>();
-    for (const [userId, activities] of Object.entries(activityMap)) {
-      if (activities.length > 0) {
-        next.set(userId, activities);
+    set((state) => {
+      const next = new Map(state.userActivities);
+      for (const [userId, activities] of Object.entries(activityMap)) {
+        if (activities.length > 0) {
+          next.set(userId, activities);
+        } else {
+          next.delete(userId);
+        }
       }
-    }
-    set({ userActivities: next });
+      return { userActivities: next };
+    });
   },
 
   setShowActivity: (show) => {