"Bayesian inference on the other hand is a specific type of statistical model where the aim is to model distributions, not just the output variable (which is what ML is traditionally focused on)." - What distribution are you referring to? One of the advantages of the Bayesian approach (in the context of models and not of probability, it is not a model, it is a way of estimating the values of the parameters of a model) is that it provides a proper statistical distribution—and not a distribution based on theoretical formulas that require certain assumption to be true to have certain properties—of parameters and model predictions.

You can read more at https://www.fharrell.com/post/stat-ml/ (Frank Harrell is a top statistician who was once a frequentist and now is a bayesian. He writes also on the differences between ML and SM and how to choose between the two)