Several interesting Dark Matter (DM) models invoke a dark sector leading to two types of relic particles, possibly interacting with each other: non-relativistic DM, and relativistic Dark Radiation (DR). These models have interesting consequences for cosmological observables, and could in principle solve problems like the small-scale cold DM crisis, Hubble tension, and/or low sigma(8) value. Their cosmological behaviour is captured by the ETHOS parametrisation, which includes a DR-DM scattering rate scaling like a power-law of the temperature, T-n. Scenarios with n = 0, 2, or 4 can easily be realised in concrete dark sector set-ups. Here we update constraints on these three scenarios using recent CMB, BAO, and high-resolution Lyman-alpha data. We introduce a new Lyman-alpha likelihood that is applicable to a wide range of cosmological models with a suppression of the matter power spectrum on small scales. For n = 2 and 4, we find that Lyman-alpha data strengthen the CMB+BAO bounds on the DM-DR interaction rate by many orders of magnitude. However, models offering a possible solution to the missing satellite problem are still compatible with our new bounds. For n = 0, high-resolution Lyman-alpha data bring no stronger constraints on the interaction rate than CMB+BAO data, except for extremely small values of the DR density. Using CMB+BAO data and a theory-motivated prior on the minimal density of DR, we find that the n = 0 model can reduce the Hubble tension from 4.1 sigma to 2.7 sigma, while simultaneously accommodating smaller values of the sigma(8) and S-8 parameters hinted by cosmic shear data.
