[utils] Improve performance using functools.cache

Closes #3786

yt_dlp/compat/functools.py

@@ -0,0 +1,12 @@
+# flake8: noqa: F405
+from functools import *  # noqa: F403
+
+from .compat_utils import passthrough_module
+
+passthrough_module(__name__, 'functools')
+del passthrough_module
+
+try:
+    cache  # >= 3.9
+except NameError:
+    cache = lru_cache(maxsize=None)