Restore hidden pass-through calls when adding asset files

CHANGES

@@ -19,6 +19,8 @@ Bugs fixed
 * Restored the the :py:class:`str` interface of the asset classes
   (``_CascadingStyleSheet`` and ``_JavaScript``), which several extensions relied upon.
   This will be removed in Sphinx 9.
+* Restored calls to ``Builder.add_{css,js}_file()``,
+  which several extensions relied upon.
 
 Testing
 -------

sphinx/application.py

@@ -5,6 +5,7 @@
 
 from __future__ import annotations
 
+import contextlib
 import os
 import pickle
 import sys
@@ -1033,6 +1034,10 @@ def add_js_file(self, filename: str | None, priority: int = 500,
             kwargs['defer'] = 'defer'
 
         self.registry.add_js_file(filename, priority=priority, **kwargs)
+        with contextlib.suppress(AttributeError):
+            self.builder.add_js_file(  # type: ignore[attr-defined]
+                filename, priority=priority, **kwargs,
+            )
 
     def add_css_file(self, filename: str, priority: int = 500, **kwargs: Any) -> None:
         """Register a stylesheet to include in the HTML output.
@@ -1093,6 +1098,10 @@ def add_css_file(self, filename: str, priority: int = 500, **kwargs: Any) -> Non
         """
         logger.debug('[app] adding stylesheet: %r', filename)
         self.registry.add_css_files(filename, priority=priority, **kwargs)
+        with contextlib.suppress(AttributeError):
+            self.builder.add_css_file(  # type: ignore[attr-defined]
+                filename, priority=priority, **kwargs,
+            )
 
     def add_latex_package(self, packagename: str, options: str | None = None,
                           after_hyperref: bool = False) -> None:

sphinx/builders/html/__init__.py

@@ -320,7 +320,8 @@ def add_css_file(self, filename: str, **kwargs: Any) -> None:
         if '://' not in filename:
             filename = posixpath.join('_static', filename)
 
-        self._css_files.append(_CascadingStyleSheet(filename, **kwargs))
+        if (asset := _CascadingStyleSheet(filename, **kwargs)) not in self._css_files:
+            self._css_files.append(asset)
 
     @property
     def script_files(self) -> list[_JavaScript]:
@@ -348,7 +349,8 @@ def add_js_file(self, filename: str, **kwargs: Any) -> None:
         if filename and '://' not in filename:
             filename = posixpath.join('_static', filename)
 
-        self._js_files.append(_JavaScript(filename, **kwargs))
+        if (asset := _JavaScript(filename, **kwargs)) not in self._js_files:
+            self._js_files.append(asset)
 
     @property
     def math_renderer_name(self) -> str | None: