[BUG]: `json.dumps` failed on object with new `_pybind11_conduit_v1` method

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What version (or hash if on master) of pybind11 are you using?

2.13.6

Problem description

A new self._pybind11_conduit_v1_() method that is added to all classes by default breaks the serialization of this object through json.dumps([object with _pybind11_conduit_v1], default=vars). I would like to clarify whether this is by mistake or intentional, considering also that this is a patch release. Thanks!

The error:

  File "/opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/triton/compiler/compiler.py", line 315, in compile
    metadata_group[metadata_filename] = fn_cache_manager.put(json.dumps(metadata, default=vars), metadata_filename,
  File "/opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/json/__init__.py", line 234, in dumps
    return cls(
  File "/opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/json/encoder.py", line 199, in encode
    chunks = self.iterencode(o, _one_shot=True)
  File "/opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/json/encoder.py", line 257, in iterencode
    return _iterencode(o, 0)
TypeError: vars() argument must have __dict__ attribute

Reproducible example code

Since this should be a problem with any object, and I have no experience with `pybind`, I will leave it without a reproducer for now, but if it is not so easy to reproduce, I may try to make one.

Is this a regression? Put the last known working version here if it is.

2.13.5

Start by reproducing the failure with Python's json.dumps(..., default=vars) on a pybind11-bound object that has pybind11_conduit_v1, then compare behavior between pybind11 2.13.5 and 2.13.6. Done means the intended serialization behavior and whether the 2.13.6 change is a regression are clearly established.