Commas in variable names cause idata writing to fail if combined with transforms

Reproducible example

import numpy as np
import pymc as pm

coords = {
    "age_group": [1, 2],
    "education": ["basic", "secondary", "higher"],
    "language_outp": ["et", "other"],
}

with pm.Model(coords=coords):
    x = pm.Normal(
        "alpha_age_group,education_offset_language",
        mu=0.0,
        sigma=1.0,
        dims=("age_group", "education", "language_outp"),
        transform=pm.distributions.transforms.ZeroSumTransform([0, 1]),
    )
    pm.Normal("y", mu=x[0, 0, 0], sigma=1.0, observed=np.array(0.0))

    pm.sample(
        draws=20,
        tune=20,
        chains=1,
        cores=1,
        progressbar=False,
        nuts_sampler="nutpie",
    )

fails with

Traceback (most recent call last):
  File "/home/velochy/salk/salk_internal_package/one_offs/replicate/nutpie_comma_dim_bug_repro.py", line 22, in <module>
    pm.sample(
  File "/home/velochy/miniconda3/envs/salk/lib/python3.12/site-packages/pymc/sampling/mcmc.py", line 832, in sample
    return _sample_external_nuts(
           ^^^^^^^^^^^^^^^^^^^^^^
  File "/home/velochy/miniconda3/envs/salk/lib/python3.12/site-packages/pymc/sampling/mcmc.py", line 377, in _sample_external_nuts
    idata = nutpie.sample(
            ^^^^^^^^^^^^^^
  File "/home/velochy/miniconda3/envs/salk/lib/python3.12/site-packages/nutpie/sample.py", line 865, in sample
    result = sampler.wait()
             ^^^^^^^^^^^^^^
  File "/home/velochy/miniconda3/envs/salk/lib/python3.12/site-packages/nutpie/sample.py", line 528, in wait
    return self._extract(results)
           ^^^^^^^^^^^^^^^^^^^^^^
  File "/home/velochy/miniconda3/envs/salk/lib/python3.12/site-packages/nutpie/sample.py", line 573, in _extract
    return _arrow_to_arviz(
           ^^^^^^^^^^^^^^^^
  File "/home/velochy/miniconda3/envs/salk/lib/python3.12/site-packages/nutpie/sample.py", line 99, in _arrow_to_arviz
    return arviz.from_dict(
           ^^^^^^^^^^^^^^^^
  File "/home/velochy/miniconda3/envs/salk/lib/python3.12/site-packages/arviz/data/io_dict.py", line 459, in from_dict
    ).to_inference_data()
      ^^^^^^^^^^^^^^^^^^^
  File "/home/velochy/miniconda3/envs/salk/lib/python3.12/site-packages/arviz/data/io_dict.py", line 334, in to_inference_data
    "posterior": self.posterior_to_xarray(),
                 ^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/velochy/miniconda3/envs/salk/lib/python3.12/site-packages/arviz/data/base.py", line 71, in wrapped
    return func(cls)
           ^^^^^^^^^
  File "/home/velochy/miniconda3/envs/salk/lib/python3.12/site-packages/arviz/data/io_dict.py", line 97, in posterior_to_xarray
    dict_to_dataset(
  File "/home/velochy/miniconda3/envs/salk/lib/python3.12/site-packages/arviz/data/base.py", line 406, in dict_to_dataset
    key: numpy_to_data_array(
         ^^^^^^^^^^^^^^^^^^^^
  File "/home/velochy/miniconda3/envs/salk/lib/python3.12/site-packages/arviz/data/base.py", line 305, in numpy_to_data_array
    coords = {key: xr.IndexVariable((key,), data=np.asarray(coords[key])) for key in dims}
                                                            ~~~~~~^^^^^
KeyError: 'education_offset_language_zerosum___dim_1'

Start by running the reproducible Python example, then inspect nutpie/sample.py at _arrow_to_arviz and the ArviZ conversion shown in the traceback. The fix is complete when the example with the comma-containing variable name and ZeroSumTransform writes inference data without the missing-coordinate KeyError.