fix: v0.9.4 inbox badge clears when seen

Opening the bell marks its events seen; viewing a session (or returning
to the tab) reads that session's events. The badge now drops to what is
live instead of climbing with every background "finished". Closes #42

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01WHRLCCdXYm41Qx5kNhehaP

web/src/inbox.js

@@ -69,7 +69,27 @@ export class Inbox {
     this.button.setAttribute('aria-expanded', String(open));
     if (!open) this.peeking = null;
     this.panel.classList.toggle('is-peek', false);
-    if (open) this.render();
+    if (open) {
+      this.render();
+      this.markSeen();
+    }
+  }
+
+  // Opening the bell counts as seeing what's in it (devdesk#42): the badge clears
+  // but the entries keep their highlight until the panel is redrawn.
+  markSeen() {
+    if (!this.events.some((e) => !e.read)) return;
+    this.events = this.events.map((e) => ({ ...e, read: true }));
+    save(this.events);
+    this.renderBadge();
+  }
+
+  // Looking at a session reads what it reported (finished, waiting) while you were away.
+  markSessionRead(session) {
+    if (!session || !this.events.some((e) => !e.read && e.session === session && !e.url)) return;
+    this.events = this.events.map((e) => (e.session === session && !e.url ? { ...e, read: true } : e));
+    save(this.events);
+    this.render();
   }
 
   // Something happened. The same kind for the same session within a minute is
@@ -102,6 +122,11 @@ export class Inbox {
   }
 
   render() {
+    this.renderBadge();
+    if (this.isOpen) this.renderPanel();
+  }
+
+  renderBadge() {
     const count = this.waiting.length + this.alerts.length + this.unread();
     const urgent = this.waiting.length > 0 || this.alerts.some((a) => a.severity === 'critical');
     this.badge.textContent = count ? String(count) : '';
@@ -114,7 +139,6 @@ export class Inbox {
         this.unread() && `${this.unread()} new event(s)`,
       ].filter(Boolean).join(' · ')
       : 'Inbox: nothing new';
-    if (this.isOpen) this.renderPanel();
   }
 
   // ------------------------------------------------------------ answer from here

web/src/main.js

@@ -181,6 +181,7 @@ function renderPanelsBadge() {
 }
 
 function onSessionData({ fetched = false } = {}) {
+  if (document.visibilityState === 'visible') inbox?.markSessionRead(state.session);
   renderUsage();
   renderSessionChip();
   renderAttention(fetched);
@@ -1074,7 +1075,10 @@ function wireChrome() {
 
   window.addEventListener('online', retrySoon);
   document.addEventListener('visibilitychange', () => {
-    if (!document.hidden) retrySoon();
+    if (!document.hidden) {
+      retrySoon();
+      inbox.markSessionRead(state.session);
+    }
   });
   // Session states feed the header chip and the notifications for other sessions,
   // so poll even in a background tab (browsers throttle that to about once a