[update] Overhaul self-updater

Authored by: bashonly, Grub4K

Co-authored-by: Simon Sawicki <contact@grub4k.xyz>

yt_dlp/YoutubeDL.py

@@ -60,7 +60,7 @@
     get_postprocessor,
 )
 from .postprocessor.ffmpeg import resolve_mapping as resolve_recode_mapping
-from .update import REPOSITORY, _get_system_deprecation, current_git_head, detect_variant
+from .update import REPOSITORY, _get_system_deprecation, _make_label, current_git_head, detect_variant
 from .utils import (
     DEFAULT_OUTTMPL,
     IDENTITY,
@@ -3928,8 +3928,7 @@ def get_encoding(stream):
         klass = type(self)
         write_debug(join_nonempty(
             f'{REPOSITORY.rpartition("/")[2]} version',
-            f'{CHANNEL.rpartition("@")[2]}@{__version__}',
-            not ORIGIN.startswith('yt-dlp/') and f'from {ORIGIN}',
+            _make_label(ORIGIN, CHANNEL.partition('@')[2] or __version__, __version__),
             f'[{RELEASE_GIT_HEAD[:9]}]' if RELEASE_GIT_HEAD else '',
             '' if source == 'unknown' else f'({source})',
             '' if _IN_CLI else 'API' if klass == YoutubeDL else f'API:{self.__module__}.{klass.__qualname__}',