[ie/instagram] Fix logged-in extraction (#17278)

Closes #17275
Authored by: bashonly

yt_dlp/extractor/instagram.py

@@ -42,7 +42,6 @@ def _id_to_pk(shortcode):
 
 
 class InstagramBaseIE(InfoExtractor):
-    _API_BASE_URL = 'https://i.instagram.com/api/v1'
     _BASE_URL = 'https://www.instagram.com/'
     _APP_IDS = {
         'ios': '124024574287414',
@@ -75,6 +74,12 @@ class InstagramBaseIE(InfoExtractor):
     def _is_web_app(self):
         return self._app_id == self._APP_IDS['web']
 
+    @property
+    def _API_BASE_URL(self):
+        if not self._is_web_app:
+            return 'https://i.instagram.com/api/v1'
+        return 'https://www.instagram.com/api/v1'
+
     @property
     def _api_headers(self):
         return {
@@ -87,7 +92,8 @@ class InstagramBaseIE(InfoExtractor):
 
     @staticmethod
     def _is_login_redirect(url):
-        return urllib.parse.urlparse(url).path.startswith('/accounts/login')
+        path = urllib.parse.urlparse(url).path
+        return path.startswith('/accounts/login') or path == '/'
 
     def _get_count(self, media, kind, *keys):
         return traverse_obj(