Updated observational constraints on spatially-flat and non-flat $\Lambda$CDM and XCDM cosmological models

We study 6 LCDM models, with 4 allowing for non-flat geometry and 3 allowing for a non-unity lensing consistency parameter $A_L$. We also study 6 XCDM models with a dynamical dark energy density X-fluid with equation of state $w$. For the non-flat models we use two different primordial power spectra, Planck $P(q)$ and new $P(q)$. These models are tested against: Planck 2018 CMB power spectra (P18) and lensing potential power spectrum (lensing), and an updated compilation of BAO, SNIa, $H(z)$, and $f\sigma_8$ data [non-CMB data]. P18 data favor closed geometry for the LCDM and XCDM models and $w<-1$ (phantom-like dark energy) for the XCDM models while non-CMB data favor open geometry for the LCDM models and closed geometry and $w>-1$ (quintessence-like dark energy) for the XCDM models. When P18 and non-CMB data are jointly analyzed there is weak evidence for open geometry and moderate evidence for quintessence-like dark energy. Regardless of data used, $A_L>1$ is always favored. The XCDM model constraints obtained from CMB data and from non-CMB data are incompatible, ruling out the 3 $A_L = 1$ XCDM models at $> 3\sigma$. In the 9 models not ruled out, for the P18+lensing+non-CMB data set we find little deviation from flat geometry and moderate deviation from $w=-1$. In all 6 non-flat models (not ruled out), open geometry is mildly favored, and in all 3 XCDM+$A_L$ models (not ruled out) quintessence-like dark energy is moderately favored (by at most $1.6 \sigma$). In the $A_L = 1$ non-flat LCDM cases, we find for P18+lensing+non-CMB data $\Omega_k = 0.0009 \pm 0.0017$ [$0.0008 \pm 0.0017$] for the Planck [new] $P(q)$ model, favoring open geometry. The flat LCDM model remains the simplest (largely) observationally-consistent cosmological model. Our cosmological parameter constraints obtained for the flat LCDM model (and other models) are the most restrictive results to date (Abridged).