[ie/PatreonCampaign] Fix `campaign_id` extraction (#10070)

Closes #10013
Authored by: bashonly

yt_dlp/extractor/patreon.py

@@ -486,7 +486,8 @@ class PatreonCampaignIE(PatreonBaseIE):
         campaign_id, vanity = self._match_valid_url(url).group('campaign_id', 'vanity')
         if campaign_id is None:
             webpage = self._download_webpage(url, vanity, headers={'User-Agent': self.USER_AGENT})
-            campaign_id = self._search_regex(r'https://www.patreon.com/api/campaigns/(\d+)/?', webpage, 'Campaign ID')
+            campaign_id = self._search_nextjs_data(
+                webpage, vanity)['props']['pageProps']['bootstrapEnvelope']['pageBootstrap']['campaign']['data']['id']
 
         params = {
             'json-api-use-default-includes': 'false',