I think each category of Bayesian described in the article generally falls under Breiman's [0] "data modeling" culture, while ML practitioners, even when using Bayesian methods, almost invariably fall under the "algorithmic modeling" culture. In particular, the article's definition of pragmatic Bayes says that "the model should be consistent with knowledge about the underlying scientific problem and the data collection process," which I don't consider the norm in ML at all.

I do think ML practitioners in general align with the "iteration" category in my characterization, though you could joke that that miscategorizes people who just use (boosted trees|transformers) for everything.

[0] https://projecteuclid.org/journals/statistical-science/volum...