[extractor/youtube] Fix parsing `comment_count` (#6523)

Closes #5849
Authored by: nick-cd

yt_dlp/extractor/youtube.py

@@ -4268,11 +4268,11 @@ class YoutubeIE(YoutubeBaseInfoExtractor):
 
         info['comment_count'] = traverse_obj(initial_data, (
             'contents', 'twoColumnWatchNextResults', 'results', 'results', 'contents', ..., 'itemSectionRenderer',
-            'contents', ..., 'commentsEntryPointHeaderRenderer', 'commentCount', 'simpleText'
+            'contents', ..., 'commentsEntryPointHeaderRenderer', 'commentCount'
         ), (
             'engagementPanels', lambda _, v: v['engagementPanelSectionListRenderer']['panelIdentifier'] == 'comment-item-section',
-            'engagementPanelSectionListRenderer', 'header', 'engagementPanelTitleHeaderRenderer', 'contextualInfo', 'runs', ..., 'text'
-        ), expected_type=int_or_none, get_all=False)
+            'engagementPanelSectionListRenderer', 'header', 'engagementPanelTitleHeaderRenderer', 'contextualInfo'
+        ), expected_type=self._get_count, get_all=False)
 
         try:  # This will error if there is no livechat
             initial_data['contents']['twoColumnWatchNextResults']['conversationBar']['liveChatRenderer']['continuations'][0]['reloadContinuationData']['continuation']