feat(desktop): add Show Dashboard tray item and empty-state copy

Linux tray implementations often do not deliver a distinct left-click event
through the AppIndicator path, so the popover could not be opened on GNOME.
Add an explicit Show Dashboard menu item that calls toggle_popover so the
UI is reachable via the tray menu on every platform.

Also render a friendly empty state in the popover when no session data is
found, pointing at the supported source paths instead of showing a bare
$0 hero with an empty activity list.

desktop/src-tauri/src/lib.rs

@@ -64,10 +64,11 @@ pub fn run() {
 }
 
 fn build_tray(app: &AppHandle) -> tauri::Result<()> {
+    let dashboard = MenuItem::with_id(app, "dashboard", "Show Dashboard", true, None::<&str>)?;
     let refresh = MenuItem::with_id(app, "refresh", "Refresh", true, None::<&str>)?;
     let report = MenuItem::with_id(app, "report", "Open Full Report", true, None::<&str>)?;
     let quit = MenuItem::with_id(app, "quit", "Quit CodeBurn", true, None::<&str>)?;
-    let menu = Menu::with_items(app, &[&refresh, &report, &quit])?;
+    let menu = Menu::with_items(app, &[&dashboard, &refresh, &report, &quit])?;
 
     TrayIconBuilder::with_id("codeburn-tray")
         .tooltip("CodeBurn")
@@ -75,6 +76,7 @@ fn build_tray(app: &AppHandle) -> tauri::Result<()> {
         .show_menu_on_left_click(false)
         .on_menu_event(|app, event| match event.id.as_ref() {
             "quit" => app.exit(0),
+            "dashboard" => toggle_popover(app),
             "refresh" => {
                 // Nudge the webview so it re-requests the payload. The front-end listens for
                 // this event and kicks off a new fetch_payload command.

desktop/src/App.tsx

@@ -124,22 +124,40 @@ export function App() {
         ))}
       </nav>
 
-      <section className="activity">
-        <h2 className="section-title">Activity</h2>
-        {payload.current.topActivities.length === 0 && (
-          <p className="empty">No activity for this period.</p>
-        )}
-        {payload.current.topActivities.map(a => (
-          <div key={a.name} className="row">
-            <div className="row-label">{a.name}</div>
-            <div className="row-cost">{formatCompactCurrency(a.cost, currency)}</div>
-            <div className="row-turns">{a.turns}</div>
-            <div className="row-oneshot">
-              {a.oneShotRate == null ? '—' : `${Math.round(a.oneShotRate * 100)}%`}
+      {!loading && payload.current.calls === 0 && payload.current.sessions === 0 ? (
+        <section className="empty-state">
+          <h2 className="section-title">No session data yet</h2>
+          <p>
+            CodeBurn reads local session logs from your AI coding tools. It looks like
+            none of the supported tools have written any sessions on this machine yet.
+          </p>
+          <p>Supported sources:</p>
+          <ul>
+            <li><code>~/.claude/projects/</code> (Claude Code)</li>
+            <li><code>~/.codex/sessions/</code> (Codex CLI)</li>
+            <li>Cursor IDE local database</li>
+            <li>GitHub Copilot session events</li>
+          </ul>
+          <p>Run one of those tools for a session, then hit Refresh.</p>
+        </section>
+      ) : (
+        <section className="activity">
+          <h2 className="section-title">Activity</h2>
+          {payload.current.topActivities.length === 0 && (
+            <p className="empty">No activity for this period.</p>
+          )}
+          {payload.current.topActivities.map(a => (
+            <div key={a.name} className="row">
+              <div className="row-label">{a.name}</div>
+              <div className="row-cost">{formatCompactCurrency(a.cost, currency)}</div>
+              <div className="row-turns">{a.turns}</div>
+              <div className="row-oneshot">
+                {a.oneShotRate == null ? '—' : `${Math.round(a.oneShotRate * 100)}%`}
+              </div>
             </div>
-          </div>
-        ))}
-      </section>
+          ))}
+        </section>
+      )}
 
       {payload.optimize.findingCount > 0 && (
         <section className="findings">

desktop/src/styles.css

@@ -157,6 +157,23 @@ html, body, #root {
 
 .empty { color: var(--text-tertiary); font-size: 10.5px; padding: var(--spacing-md) 0; }
 
+.empty-state {
+  padding: var(--spacing-md) var(--spacing-lg) var(--spacing-lg);
+  color: var(--text-secondary);
+  font-size: 11.5px;
+  line-height: 1.55;
+}
+.empty-state p { margin: 0 0 8px 0; }
+.empty-state ul { margin: 0 0 10px 0; padding-left: 18px; }
+.empty-state li { margin-bottom: 2px; }
+.empty-state code {
+  font-family: var(--font-mono);
+  font-size: 10.5px;
+  background: rgba(255, 255, 255, 0.04);
+  padding: 1px 4px;
+  border-radius: 3px;
+}
+
 /* ---- findings ---- */
 .findings { padding: 0 var(--spacing-lg) var(--spacing-sm); }
 .findings-cta {