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We present new cosmological constraints in a set of motivated extensions ofthe $\Lambda$CDM model using the polarization and gravitational lensingmeasurements from the South Pole Telescope and the Planck CMB temperatureobservations at large angular scales. In all cosmological scenarios, this CMBdata brings the clustering measurements into agreement with the low-redshiftprobes of large-scale structure. Combining the SPT-3G, SPTpol and Plancklarge-scale temperature data with the latest full-shape BOSS and BAOmeasurements, information from the weak lensing and photometric galaxyclustering, and Pantheon supernova set we find a $4\sigma$ evidence for nonzeroneutrino mass, $\sum m_\nu=0.22\pm0.06\,{\rm eV}$.Breaking the CMB degeneraciesbetween $\sum m_\nu$ and the cosmological parameters by the BOSS data is amajor contribution to our neutrino mass measurement. The future CMB data wouldallow for investigating this measurement. Then we explore the possibility ofdynamical dark energy with two model-independent approaches: one introduces aphantom crossing in dark energy equation of state, another provides with asharp transition in the dark energy evolution. For the combination of all dataconsidered, the both models predict $H_0\simeq68\,{\rm km\,s^{-1}Mpc^{-1}}$being in a $\sim3\sigma$ tension with the SH0ES constraint. However, when thelocal Type Ia supernovae are calibrated by Cepheids, the late Universescenarios suggest significantly higher values of $H_0$ consistent with SH0ES.Our work draws attention to the supernova absolute magnitude calibration as oneof the issues on the way to reconcile the $H_0$ tension.

Exploring ${\Lambda}$CDM extensions with SPT-3G and Planck data:  4$\sigma$ evidence for neutrino masses and implications of extended dark  energy models for cosmological tensions