reverted:
--- b/modules/paragraphs_library/tests/src/FunctionalJavascript/ParagraphsLibraryItemEntityBrowserTest.php
+++ a/modules/paragraphs_library/tests/src/FunctionalJavascript/ParagraphsLibraryItemEntityBrowserTest.php
@@ -3,7 +3,6 @@
 namespace Drupal\Tests\paragraphs_library\FunctionalJavascript;
 
 use Drupal\language\Entity\ConfigurableLanguage;
-use Drupal\paragraphs\Entity\ParagraphsType;
 use Drupal\Tests\entity_browser\FunctionalJavascript\EntityBrowserWebDriverTestBase;
 use Drupal\Tests\paragraphs\FunctionalJavascript\ParagraphsTestBaseTrait;
 
@@ -219,21 +218,6 @@
     $save_button->press();
     $this->waitForAjaxToFinish();
     $this->assertSession()->fieldExists('paragraphs[0][subform][field_text][0][value]');
-
-    // Check the Library item unpublished indicator.
-    ParagraphsType::load('text')
-      ->setThirdPartySetting('paragraphs_library', 'allow_library_conversion', TRUE)
-      ->save();
-    $this->drupalGet('node/add');
-    $title = $this->assertSession()->fieldExists('Title');
-    $title->setValue('Paragraph test');
-    $this->getSession()->getPage()->pressButton('field_paragraphs_text_add_more');
-    $this->waitForAjaxToFinish();
-    $this->getSession()->getPage()->fillField('field_paragraphs[0][subform][field_text][0][value]', 'This is a reusable text UPDATED.');
-    $dropdown = $this->assertSession()->elementExists('css', '.paragraphs-dropdown');
-    $dropdown->click();
-    $this->getSession()->getPage()->pressButton('Promote to library');
-    $this->assertSession()->elementExists('css', '.paragraph-formatter .paragraphs-icon-view');
   }
 
 }
only in patch2:
unchanged:
--- a/modules/paragraphs_library/tests/src/FunctionalJavascript/ParagraphsContentModerationTest.php
+++ b/modules/paragraphs_library/tests/src/FunctionalJavascript/ParagraphsContentModerationTest.php
@@ -3,6 +3,7 @@
 namespace Drupal\Tests\paragraphs_library\FunctionalJavascript;
 
 use Behat\Mink\Element\Element;
+use Drupal\paragraphs\Entity\ParagraphsType;
 use Drupal\Tests\field_ui\Traits\FieldUiTestTrait;
 use Drupal\FunctionalJavascriptTests\WebDriverTestBase;
 use Drupal\Tests\paragraphs\FunctionalJavascript\ParagraphsTestBaseTrait;
@@ -421,6 +422,31 @@ class ParagraphsContentModerationTest extends WebDriverTestBase {
     $assert_session->pageTextContains('Content types');
     $assert_session->elementNotExists('css', 'a[href$="' . $this->workflow->id() . '/type/paragraph"]');
     $assert_session->elementExists('css', 'a[href$="' . $this->workflow->id() . '/type/node"]');
+
+    // Check the library item is marked as unpublished.
+    $form_display = \Drupal::service('entity_display.repository')->getFormDisplay('node', 'paragraphed_moderated_test');
+    $form_display = $form_display->setComponent('field_paragraphs', ['type' => 'paragraphs']);
+    $form_display->save();
+    // Check the Library item unpublished indicator.
+    ParagraphsType::load('text')
+      ->setThirdPartySetting('paragraphs_library', 'allow_library_conversion', TRUE)
+      ->save();
+    $this->drupalGet('node/add');
+    $title = $this->assertSession()->fieldExists('Title');
+    $title->setValue('Paragraph test');
+    $element = $this->getSession()->getPage()->find('xpath', '//*[contains(@class, "dropbutton-toggle")]');
+    $element->click();
+    $button = $this->getSession()->getPage()->findButton('Add text');
+    $button->press();
+    $assert_session->assertWaitOnAjaxRequest();
+    $this->getSession()->getPage()->fillField('field_paragraphs[0][subform][field_text][0][value]', 'This is a reusable text UPDATED.');
+    $first_row = $this->assertSession()->elementExists('css', '#field-paragraphs-add-more-wrapper tr.draggable:nth-of-type(1)');
+    $dropdown = $this->assertSession()->elementExists('css', '.paragraphs-dropdown', $first_row);
+    $dropdown->click();
+    $this->getSession()->getPage()->pressButton('Promote to library');
+    $assert_session->assertWaitOnAjaxRequest();
+    $style_selector = $this->getSession()->getPage()->find('css', '.paragraph-formatter .paragraphs-icon-view');
+    $this->assertTrue($style_selector->isVisible());
   }
 
   /**