We have seminar courses for this where master students do some lit review (mainly based around one paper) and present that work in a longer form writing.
This is also "just" learning by doing. There is some back-and-forth with PhD students who help with the structure, but there's no explicit instruction.
This seemed to be quite needed for students to get up to speed. I was from Finland, where this subject was brought up before uni.
For what it's worth, I remember my supervisor calling bullshit on my then dense and overly academic writing and I thank them for it. It was a process of un-learning bad patterns or preconcieved notions about the writing process.
Recommend.