Improve catalog view with relative timestamps, auto-refresh, and installed badges

Show app count with relative last-refreshed time in subtitle. Auto-refresh
catalog on first visit when empty. Show "Installed" badge on catalog entries
that match already-installed AppImages instead of the Install button.

src/ui/catalog_view.rs

@@ -95,20 +95,10 @@ pub fn build_catalog_page(db: &Rc<Database>) -> adw::NavigationPage {
     stack.add_named(&scrolled, Some("results"));
 
     // Show empty or results based on catalog data
-    let sources = catalog::get_sources(db);
-    let enabled_sources: Vec<_> = sources.iter().filter(|s| s.enabled).collect();
     let app_count = db.catalog_app_count().unwrap_or(0);
     if app_count > 0 {
         stack.set_visible_child_name("results");
-        if let Some(src) = enabled_sources.first() {
+        update_catalog_subtitle(&title, app_count);
-            let synced = src.last_synced.as_deref().unwrap_or("never");
-            title.set_subtitle(&format!(
-                "{} apps from {} ({}), synced: {}",
-                src.app_count, src.name, src.source_type.as_str(), synced,
-            ));
-        } else {
-            title.set_subtitle(&format!("{} apps available", app_count));
-        }
     } else {
         stack.set_visible_child_name("empty");
     }
@@ -195,7 +185,7 @@ pub fn build_catalog_page(db: &Rc<Database>) -> adw::NavigationPage {
                         toast_c.add_toast(adw::Toast::new(
                             &format!("Catalog refreshed: {} apps", count),
                         ));
-                        title_c.set_subtitle(&format!("{} apps available", count));
+                        update_catalog_subtitle(&title_c, count as i64);
                         stack_c.set_visible_child_name("results");
                         populate_categories(&db_c, &cat_box_c, &active_cat_c, &results_c, &search_c);
                         populate_results(&db_c, "", None, &results_c, &toast_c);
@@ -221,6 +211,11 @@ pub fn build_catalog_page(db: &Rc<Database>) -> adw::NavigationPage {
     wire_refresh(&refresh_btn);
     wire_refresh(&refresh_header_btn);
 
+    // Auto-refresh on first visit when catalog is empty
+    if app_count == 0 {
+        refresh_btn.emit_clicked();
+    }
+
     adw::NavigationPage::builder()
         .title(&i18n("Catalog"))
         .tag("catalog")
@@ -228,6 +223,18 @@ pub fn build_catalog_page(db: &Rc<Database>) -> adw::NavigationPage {
         .build()
 }
 
+/// Update the catalog subtitle to show app count and relative last-refreshed time.
+fn update_catalog_subtitle(title: &adw::WindowTitle, app_count: i64) {
+    let settings = gtk::gio::Settings::new(crate::config::APP_ID);
+    let last_refreshed = settings.string("catalog-last-refreshed");
+    if last_refreshed.is_empty() {
+        title.set_subtitle(&format!("{} apps available", app_count));
+    } else {
+        let relative = widgets::relative_time(&last_refreshed);
+        title.set_subtitle(&format!("{} apps - Refreshed {}", app_count, relative));
+    }
+}
+
 fn populate_results(
     db: &Rc<Database>,
     query: &str,
@@ -254,6 +261,14 @@ fn populate_results(
     let toast_ref = toast_overlay.clone();
     let db_ref = db.clone();
 
+    // Get installed app names for matching
+    let installed_names: std::collections::HashSet<String> = db
+        .get_all_appimages()
+        .unwrap_or_default()
+        .iter()
+        .filter_map(|r| r.app_name.as_ref().map(|n| n.to_lowercase()))
+        .collect();
+
     for app in &results {
         let row = adw::ActionRow::builder()
             .title(&app.name)
@@ -280,6 +295,16 @@ fn populate_results(
             }
         }
 
+        // Show "Installed" badge if already installed, otherwise show Install button
+        let is_installed = installed_names.contains(&app.name.to_lowercase());
+        if is_installed {
+            let installed_badge = widgets::status_badge(&i18n("Installed"), "success");
+            installed_badge.set_valign(gtk::Align::Center);
+            row.add_suffix(&installed_badge);
+            list_box.append(&row);
+            continue;
+        }
+
         // Install button
         let install_btn = gtk::Button::builder()
             .label(&i18n("Install"))