[extractor] Show video id in error messages if possible

yt_dlp/utils.py

@@ -2399,25 +2399,27 @@ network_exceptions = tuple(network_exceptions)
 class ExtractorError(YoutubeDLError):
     """Error during info extraction."""
 
-    def __init__(self, msg, tb=None, expected=False, cause=None, video_id=None):
+    def __init__(self, msg, tb=None, expected=False, cause=None, video_id=None, ie=None):
         """ tb, if given, is the original traceback (so that it can be printed out).
         If expected is set, this is a normal error message and most likely not a bug in yt-dlp.
         """
-
         if sys.exc_info()[0] in network_exceptions:
             expected = True
-        if video_id is not None:
-            msg = video_id + ': ' + msg
-        if cause:
-            msg += ' (caused by %r)' % cause
-        if not expected:
-            msg += bug_reports_message()
-        super(ExtractorError, self).__init__(msg)
 
+        self.msg = msg
         self.traceback = tb
-        self.exc_info = sys.exc_info()  # preserve original exception
+        self.expected = expected
         self.cause = cause
         self.video_id = video_id
+        self.ie = ie
+        self.exc_info = sys.exc_info()  # preserve original exception
+
+        super(ExtractorError, self).__init__(''.join((
+            format_field(ie, template='[%s] '),
+            format_field(video_id, template='%s: '),
+            msg,
+            format_field(cause, template=' (caused by %r)'),
+            '' if expected else bug_reports_message())))
 
     def format_traceback(self):
         if self.traceback is None: