TypeError(f'{name!r} is a field but has no type annotation')

Describe the bug

* Sphinx version:   8.2.0
* Docutils version: 0.23
* Jinja2 version:   3.1.5
* Pygments version: 2.14.0 (will shortly update to 2.20)

Traceback
=========

Traceback (most recent call last):
  File "/usr/lib/python3.12/site-packages/sphinx/cmd/build.py", line 414, in build_main
    app = Sphinx(
  File "/usr/lib/python3.12/site-packages/sphinx/application.py", line 286, in __init__
    self.setup_extension(extension)
  File "/usr/lib/python3.12/site-packages/sphinx/application.py", line 490, in setup_extension
    self.registry.load_extension(self, extname)
  File "/usr/lib/python3.12/site-packages/sphinx/registry.py", line 541, in load_extension
    mod = import_module(extname)
  File "/usr/lib/python3.12/importlib/__init__.py", line 126, in import_module
    return _bootstrap._gcd_import(name[level:], package, level)
  File "<frozen importlib._bootstrap>", line 1050, in _gcd_import
  File "<frozen importlib._bootstrap>", line 1027, in _find_and_load
  File "<frozen importlib._bootstrap>", line 1006, in _find_and_load_unlocked
  File "<frozen importlib._bootstrap>", line 688, in _load_unlocked
  File "<frozen importlib._bootstrap_external>", line 883, in exec_module
  File "<frozen importlib._bootstrap>", line 241, in _call_with_frames_removed
  File "/usr/lib/python3.12/site-packages/sphinx/builders/epub3.py", line 16, in <module>
    from sphinx.builders import _epub_base
  File "/usr/lib/python3.12/site-packages/sphinx/builders/_epub_base.py", line 19, in <module>
    from sphinx.builders.html import StandaloneHTMLBuilder
  File "/usr/lib/python3.12/site-packages/sphinx/builders/html/__init__.py", line 43, in <module>
    from sphinx.search import js_index
  File "/usr/lib/python3.12/site-packages/sphinx/search/__init__.py", line 211, in <module>
    class WordStore:
  File "/usr/lib/python3.12/dataclasses.py", line 1185, in dataclass
    return wrap(cls)
  File "/usr/lib/python3.12/dataclasses.py", line 1176, in wrap
    return _process_class(cls, init, repr, eq, order, unsafe_hash,
  File "/usr/lib/python3.12/dataclasses.py", line 980, in _process_class
    raise TypeError(f'{name!r} is a field but has no type annotation')
TypeError: 'words' is a field but has no type annotation

How to Reproduce

docs building step of vdirsyncer:

sphinx-build -b man docs/ build/

https://aur.archlinux.org/cgit/aur.git/plain/PKGBUILD?h=vdirsyncer-git

Environment Information

I won't use pip, only my distro's packaging.

Sphinx extensions

Additional context

No response

Start with sphinx/search/init.py and the WordStore declaration named in the traceback, then reproduce with sphinx-build -b man docs/ build/ from vdirsyncer. Trace the dataclass processing that raises the error and verify that the same documentation build completes successfully after the issue is addressed.