Is the $w_0w_a$CDM cosmological parameterization evidence for dark energy dynamics partially caused by the excess smoothing of Planck PR4 CMB anisotropy data?

We study the performance of the flat $\Lambda$CDM model and the dynamical dark energy parameterizations $w_0$CDM and $w_0w_a$CDM, in which the dark energy (DE) equation of state is either constant ($w=w_0$) or redshift-dependent [$w(z)=w_0+w_a z/(1+z)$], without and with a varying CMB lensing consistency parameter $A_L$, using combinations of Planck PR4 CMB data (PR4 and lensing), and a compilation of non-CMB data composed of baryon acoustic oscillation (BAO) data that do not include DESI BAO data, Pantheon+ type Ia supernova observations, Hubble parameter measurements $H(z)$, and growth rate $f\sigma_8$ data. We also compare results from earlier Planck PR3 data with those obtained using PR4 data in order to assess the stability of cosmological constraints. For the largest data combinations, PR3/PR4+lensing+non-CMB, the cosmological parameters inferred from PR3 and PR4 data are consistent, almost all differing by $1\sigma$ or less. For the $\Lambda$CDM$+A_L$ model, we have $A_L=1.087 \pm 0.035$ for PR3 and $A_L=1.053 \pm 0.034$ ($1.6\sigma$ above unity) for PR4, which indicates that the CMB lensing anomaly is reduced when PR4 data are used. For the $w_0 w_a$CDM parameterization, we find $w_0 = -0.863\pm0.060$ (quintessence-like) and $w_0+w_a=-1.37^{+0.19}_{-0.17}$ (phantom-like), suggesting that the current observations favor dynamical DE over a cosmological constant at about $1.8\sigma$. For the $w_0w_a$CDM$+A_L$ parameterization, we find $w_0=-0.877\pm 0.060$ and $w_0 + w_a =-1.29_{-0.17}^{+0.20}$, corresponding to a preference for dynamical DE over a cosmological constant of about $1.5\sigma$ and with $A_L = 1.042 \pm 0.037$ exceeding unity at $1.1\sigma$. These results indicate that while the PR4 data mildly favor a time-evolving DE, part of this preference may be associated with possible residual excess smoothing present in the Planck PR4 CMB anisotropy spectra (abridged).