Not all approaches to the Hubble tension are equally good or bad. Some recent discussion seems to ignore the fact that early-time approaches like New Early Dark Energy also fit the CMB better than Lambda-CDM independent of the Hubble tension ( https://arxiv.org/abs/2305.08895 ).
Nice paper from Kyoto today, https://arxiv.org/abs/2309.02288, emphasizing that small-scale inhomogeneities are unlikely to play a relevant role in understanding the Hubble tension. This also follows from classic papers like BNSZ’s https://arxiv.org/abs/1004.2488 and Peebles https://arxiv.org/abs/0910.5142
Nice informative result in today’s paper; the old Early Dark Energy model struggles to address the S8 tension (https://arxiv.org/abs/2309.00401). This singles out New Early Dark Energy, a triggered phase transition in the dark sector, as a possible minimal resolution to both the H0 and the S8 tensions — see f.ex. https://arxiv.org/abs/2305.08895.