Show update count badge on Updates tab in ViewSwitcherBar

Add updatable_count() database method and refresh_update_badge()
window method. The Updates tab now shows a numeric badge with the
number of available updates and highlights with needs_attention.

src/core/database.rs

@@ -1257,6 +1257,16 @@ impl Database {
         Ok(())
     }
 
+    pub fn updatable_count(&self) -> i64 {
+        self.conn
+            .query_row(
+                "SELECT COUNT(*) FROM appimages WHERE latest_version IS NOT NULL",
+                [],
+                |row| row.get(0),
+            )
+            .unwrap_or(0)
+    }
+
     pub fn get_appimages_with_updates(&self) -> SqlResult<Vec<AppImageRecord>> {
         let sql = format!(
             "SELECT {} FROM appimages WHERE latest_version IS NOT NULL

src/window.rs

@@ -1114,6 +1114,9 @@ impl DriftwoodWindow {
                 }
             }
         });
+
+        // Update badge on Updates tab
+        self.refresh_update_badge();
     }
 
     fn trigger_scan(&self) {
@@ -1317,6 +1320,19 @@ impl DriftwoodWindow {
         });
     }
 
+    /// Update the badge number on the Updates tab in the ViewSwitcherBar.
+    fn refresh_update_badge(&self) {
+        let db = self.database();
+        let count = db.updatable_count();
+        if let Some(view_stack) = self.imp().view_stack.get() {
+            if let Some(child) = view_stack.child_by_name("updates") {
+                let page = view_stack.page(&child);
+                page.set_badge_number(count as u32);
+                page.set_needs_attention(count > 0);
+            }
+        }
+    }
+
     fn start_file_watcher(&self) {
         let settings = self.settings();
         let dirs: Vec<std::path::PathBuf> = settings