fix(docs[spa-nav]): update brand links and logo srcs after SPA navigation

why: The sidebar brand link, mobile header brand link, and logo image
srcs use relative paths that go stale after SPA navigation across
directory depths. They live outside the swap regions (.article-container,
.sidebar-tree, .toc-drawer) so swap() never updates them.
what:
- After swapping content regions, copy brand href and logo src from
  the fetched document (which has correct relative paths for the target)
- Covers: .sidebar-brand href, .header-center a href, .sidebar-logo src

Author: tony

docs/_static/js/spa-nav.js

@@ -132,6 +132,24 @@
     );
     var title = doc.querySelector("title");
     if (title) document.title = title.textContent || "";
+
+    // Brand links and logo images live outside swapped regions.
+    // Their relative hrefs/srcs go stale after cross-depth navigation.
+    // Copy the correct values from the fetched document.
+    [".sidebar-brand", ".header-center a"].forEach(function (sel) {
+      var fresh = doc.querySelector(sel);
+      if (!fresh) return;
+      document.querySelectorAll(sel).forEach(function (el) {
+        el.setAttribute("href", fresh.getAttribute("href"));
+      });
+    });
+    var freshLogos = doc.querySelectorAll(".sidebar-logo");
+    var staleLogos = document.querySelectorAll(".sidebar-logo");
+    freshLogos.forEach(function (fresh, i) {
+      if (staleLogos[i]) {
+        staleLogos[i].setAttribute("src", fresh.getAttribute("src"));
+      }
+    });
   }
 
   function reinit() {