Keep gem repos pages in sync

Signed-off-by: Alex Peterson <26804013+AMZN-alexpete@users.noreply.github.com>

Code/Tools/ProjectManager/Source/EngineScreenCtrl.cpp

@@ -39,6 +39,10 @@ namespace O3DE::ProjectManager
 
         m_tabWidget->addTab(m_engineSettingsScreen, tr("General"));
         m_tabWidget->addTab(m_gemRepoScreen, tr("Gem Repositories"));
+
+        // when tab changes, notify the current screen so it can refresh
+        connect(m_tabWidget, &QTabWidget::currentChanged, this, &EngineScreenCtrl::TabChanged);
+
         topBarHLayout->addWidget(m_tabWidget);
 
         vLayout->addWidget(topBarFrameWidget);
@@ -46,6 +50,11 @@ namespace O3DE::ProjectManager
         setLayout(vLayout);
     }
 
+    void EngineScreenCtrl::TabChanged([[maybe_unused]] int index)
+    {
+        NotifyCurrentScreen();
+    }
+
     ProjectManagerScreen EngineScreenCtrl::GetScreenEnum()
     {
         return ProjectManagerScreen::UpdateProject;
@@ -71,6 +80,15 @@ namespace O3DE::ProjectManager
         return false;
     }
 
+    void EngineScreenCtrl::NotifyCurrentScreen()
+    {
+        ScreenWidget* screen = reinterpret_cast<ScreenWidget*>(m_tabWidget->currentWidget());
+        if (screen)
+        {
+            screen->NotifyCurrentScreen();
+        }
+    }
+
     void EngineScreenCtrl::GoToScreen(ProjectManagerScreen screen)
     {
         if (screen == m_engineSettingsScreen->GetScreenEnum())