[twitch] Fix authentication and error capture (closes #14090, closes #15264)

youtube_dl/extractor/twitch.py

@@ -85,10 +85,15 @@ def login_step(page, urlh, note, data):
                 if isinstance(e.cause, compat_HTTPError) and e.cause.code == 400:
                     response = self._parse_json(
                         e.cause.read().decode('utf-8'), None)
-                    fail(response['message'])
+                    fail(response.get('message') or response['errors'][0])
                 raise
 
-            redirect_url = urljoin(post_url, response['redirect'])
+            if 'Authenticated successfully' in response.get('message', ''):
+                return None, None
+
+            redirect_url = urljoin(
+                post_url,
+                response.get('redirect') or response['redirect_path'])
             return self._download_webpage_handle(
                 redirect_url, None, 'Downloading login redirect page',
                 headers=headers)
@@ -106,6 +111,10 @@ def login_step(page, urlh, note, data):
                 'password': password,
             })
 
+        # Successful login
+        if not redirect_page:
+            return
+
         if re.search(r'(?i)<form[^>]+id="two-factor-submit"', redirect_page) is not None:
             # TODO: Add mechanism to request an SMS or phone call
             tfa_token = self._get_tfa_info('two-factor authentication token')