Show channel counts in the left CategoryNav sidebar (Feed/Channels/Saved)

Same "channels per category" counts as the categories management page,
now next to each button in the sidebar used across all three pages.
Categories already carry channel_count; "Все"/"Без категории" counts are
derived client-side from one extra unfiltered channels query, reused
across the three pages via a shared ['channels', 'all-for-counts'] key.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

frontend/src/App.css

@@ -63,6 +63,10 @@
 }
 
 .category-nav button {
+  display: flex;
+  align-items: center;
+  justify-content: space-between;
+  gap: 8px;
   text-align: left;
   padding: 6px 10px;
   border: none;
@@ -76,6 +80,14 @@
   font-weight: 600;
 }
 
+.category-nav-count {
+  font-size: 11px;
+  color: #999;
+  background: #eee;
+  border-radius: 8px;
+  padding: 1px 6px;
+}
+
 .content {
   flex: 1;
   min-width: 0;