BUG: constant_data is missing from idata when sampling with nutpie

Describe the issue:

I recently encountered an issue when trying to add constant data to some of my models.
When sampling with nuts_sampler="pymc", idata contains a group denominated as constant_data where x and y from this toy example are stored. Unfortunately, when using nutpie, the constant data is nowhere to be found.
Is this actually a bug or is there something wrong with my definitions? Or are pm.ConstantData() and such perhaps just not supported when using nutpie?
Any help would be much appreciated.

Reproduceable code example:

import numpy as np
import pymc as pm
import pytensor.tensor as pt

x = np.array([1,2,3,4])
y = np.array([100, 190, 310, 405])

with pm.Model() as pmodel:
    # add data to the pmodel as ConstantData
    pm.ConstantData("x", x)
    pm.ConstantData("y", y)

    var = pm.Normal("var", 100, 5)
    
    # likelihood
    pm.Normal("L", mu=y, sigma=0.1, observed=y)
    # posterior
    pst = x * var
    pst = pm.Deterministic("posterior", pst)
    # sampling
    idata = pm.sample(nuts_sampler="nutpie", tune=50, draws=50)

print(idata)

Error message:

Output of print(idata):

Inference data with groups:
	> posterior
	> sample_stats

Warmup iterations saved (warmup_*).

PyMC version information:

PyMC v5.8.1 (pypi)
nutpie v0.9.1 (pypi)
PyTensor v2.16.2 (pypi)

Context for the issue:

No response

Start with the provided reproducible model and compare the idata groups produced by nuts_sampler="pymc" and nuts_sampler="nutpie". Investigate how pm.ConstantData() is represented during nutpie sampling; done means the nutpie result includes the expected constant_data group containing x and y.