Use `UPDATE_HINT`

yt_dlp/update.py

@@ -182,11 +182,13 @@ def _get_version_age_warning():
         if len(version_parts) < 3:
             return None
 
+        update_message = UPDATE_HINT or 'Run "yt-dlp --update" to update'
+
         if dt.date(*version_parts[:3]) < dt.date.today() - dt.timedelta(days=90):
             return ('\n         '.join((
                 f'Your yt-dlp version ({__version__}) is older than 90 days!',
                 'It is strongly recommeded to always use the latest versions, as sites regularly change and extractors need to be adjusted.',
-                'Run "yt-dlp --update" to update. To suppress this warning, add "--no-update" to your command/config.')))
+                f'{update_message}. To suppress this warning, add "--no-update" to your command/config.')))
     except (ValueError, TypeError):
         pass