Fix search dropdown behaviour

After this change:

| Scenario | Behavior |
|----------|----------|
| Type search, click result | Navigate without `?q=`, clean URL without dropdown |
| Type search, press Enter | Navigate without `?q=`, clean URL without dropdown |
| Land on URL with `?q=` param | Show dropdown with pre-filled query |
| Click outside dropdown | Hide dropdown, keep input value |
| Focus input with existing query | Show dropdown again |

Author: st0012

lib/rdoc/generator/template/aliki/js/aliki.js

@@ -67,15 +67,7 @@ function createSearchInstance(input, result) {
   }
 
   search.select = function(result) {
-    let href = result.firstChild.firstChild.href;
-    const query = this.input.value;
-    if (query) {
-      const url = new URL(href, window.location.origin);
-      url.searchParams.set('q', query);
-      url.searchParams.set('nav', '0');
-      href = url.toString();
-    }
-    window.location.href = href;
+    window.location.href = result.firstChild.firstChild.href;
   }
 
   search.scrollIntoView = search.scrollInWindow;
@@ -97,15 +89,27 @@ function hookSearch() {
   const search = createSearchInstance(input, result);
   if (!search) return;
 
+  // Hide search results when clicking outside the search area
+  document.addEventListener('click', (e) => {
+    if (!e.target.closest('.navbar-search-desktop')) {
+      result.setAttribute('aria-expanded', 'false');
+    }
+  });
+
+  // Show search results when focusing on input (if there's a query)
+  input.addEventListener('focus', () => {
+    if (input.value.trim()) {
+      result.setAttribute('aria-expanded', 'true');
+    }
+  });
+
   // Check for ?q= URL parameter and trigger search automatically
   if (typeof URLSearchParams !== 'undefined') {
     const urlParams = new URLSearchParams(window.location.search);
     const queryParam = urlParams.get('q');
     if (queryParam) {
-      const navParam = urlParams.get('nav');
-      const autoSelect = navParam !== '0';
       input.value = queryParam;
-      search.search(queryParam, autoSelect);
+      search.search(queryParam, false);
     }
   }
 }
@@ -378,9 +382,7 @@ function hookSearchModal() {
     if (queryParam && isSmallViewport) {
       openSearchModal();
       searchInput.value = queryParam;
-      const navParam = urlParams.get('nav');
-      const autoSelect = navParam !== '0';
-      mobileSearch.search(queryParam, autoSelect);
+      mobileSearch.search(queryParam, false);
     }
   }
 }