[ie/youtube] Fix `comment_count` extraction (#11274)

Authored by: bashonly

yt_dlp/extractor/youtube.py

@@ -4701,11 +4701,12 @@ class YoutubeIE(YoutubeBaseInfoExtractor):
                 headers=self.generate_api_headers(ytcfg=master_ytcfg),
                 note='Downloading initial data API JSON')
 
+        COMMENTS_SECTION_IDS = ('comment-item-section', 'engagement-panel-comments-section')
         info['comment_count'] = traverse_obj(initial_data, (
             'contents', 'twoColumnWatchNextResults', 'results', 'results', 'contents', ..., 'itemSectionRenderer',
             'contents', ..., 'commentsEntryPointHeaderRenderer', 'commentCount',
         ), (
-            'engagementPanels', lambda _, v: v['engagementPanelSectionListRenderer']['panelIdentifier'] == 'comment-item-section',
+            'engagementPanels', lambda _, v: v['engagementPanelSectionListRenderer']['panelIdentifier'] in COMMENTS_SECTION_IDS,
             'engagementPanelSectionListRenderer', 'header', 'engagementPanelTitleHeaderRenderer', 'contextualInfo',
         ), expected_type=self._get_count, get_all=False)