Ladybird+LibWebView: Ensure existing Inspector widgets inspect the page

If the Inspector widget already exists, be sure to inspect the page when
it is re-opened. However, this should be a no-op if the page was already
inspected (as any existing Inspector will be reset if a new page load
began).

Note this is not an issue in the AppKit chrome.

Ladybird/Qt/Tab.cpp

@@ -750,6 +750,8 @@ void Tab::show_inspector_window(InspectorTarget inspector_target)
 {
     if (!m_inspector_widget)
         m_inspector_widget = new InspectorWidget(this, view());
+    else
+        m_inspector_widget->inspect();
 
     m_inspector_widget->show();
     m_inspector_widget->activateWindow();

Userland/Applications/Browser/Tab.cpp

@@ -923,6 +923,8 @@ void Tab::show_inspector_window(Browser::Tab::InspectorTarget inspector_target)
         };
 
         m_dom_inspector_widget = window->set_main_widget<InspectorWidget>(*m_web_content_view);
+    } else {
+        m_dom_inspector_widget->inspect();
     }
 
     if (inspector_target == InspectorTarget::HoveredElement) {

Userland/Libraries/LibWebView/InspectorClient.cpp

@@ -174,7 +174,9 @@ InspectorClient::~InspectorClient()
 
 void InspectorClient::inspect()
 {
-    m_dom_tree_loaded = false;
+    if (m_dom_tree_loaded)
+        return;
+
     m_content_web_view.inspect_dom_tree();
     m_content_web_view.inspect_accessibility_tree();
 }