Incorrect `objects.inv` produced for `singlehtml`

[Kodiologist]

Describe the bug

I haven't been able to get Intersphinx links to objects in Hyrule to work. I think this is because Hyrule uses the singlehtml builder and the generated objects.inv in this case has spurious anchors.

How to Reproduce

#!/bin/sh
mkdir testp
cd testp
mkdir mylib
printf 'def foo():\n "my docstring"\n return 1\n' >mylib/__init__.py
printf '.. automodule:: mylib\n  :members:\n' >index.rst
echo 'extensions = ["sphinx.ext.autodoc"]' >conf.py
mkdir build
PYTHONPATH=. sphinx-build . _build -b singlehtml
python3 -msphinx.ext.intersphinx _build/objects.inv

Expected behavior

I expected index.html#module-mylib in the output, as with the html builder, instead of index.html#document-index#module-mylib.

Your project

See the shell script above.

Screenshots

No response

OS

Ubuntu 21.10

Python version

3.9.7

Sphinx version

4.3.2

Sphinx extensions

sphinx.ext.autodoc

Extra tools

No response

Additional context

No response

[jdillard]

I don't know if things have changed in more recent versions, but index.html doesn't appear included in the objects file anymore, making it break intersphinx links where the webserver doesn't redirect for a missing index.html in the URL.