  We present an updated analysis of eleven cosmological models that may help
reduce the Hubble tension, which now reaches the $6\sigma$ level when
considering the latest SH0ES measurement versus recent CMB and BAO data,
assuming $\Lambda$CDM. Specifically, we look at five classical extensions of
$\Lambda$CDM (with massive neutrinos, spatial curvature, free-streaming or
self-interacting relativistic relics, or dynamical dark energy) and six
elaborate models featuring either a time-varying electron mass, early dark
energy or some non-trivial interactions in the neutrino sector triggered by a
light Majoron. We improve over previous works in several ways. We include the
latest data from the South Pole Telescope as well as the most recent
measurement of the Hubble rate by the SH0ES collaboration. We treat the summed
neutrino mass as a free parameter in most of our models, which reveals
interesting degeneracies and constraints. We define additional metrics to
assess the potential of a model to reduce or even solve the Hubble tension. We
validate an emulator that uses active learning to train itself during each
parameter inference run for any arbitrary model. We find that the time-varying
electron mass and the Majoron models are now ruled out at more than $3\sigma$.
Models with a time-varying electron mass and spatial curvature or with early
dark energy reduce the tension to $1.0-2.9\sigma$. Nevertheless, none of the
models considered in this work is favored with enough statistical significance
to become the next concordance model of Cosmology.
