I'm probably not the most qualified since I'm a PhD student, but in my experience it's generally an ML position where the description requires you to have some domain knowledge or a position title in the application domain that specifies that you're doing ML.

Try more applied fields!

Not in industry (PhD student), but used to do deep learning type research with a computer vision background. I'm now working on applying ML for computer systems. At least 90% of my actual research work is building the system, collecting the data, and deciding how to frame the problem; for that last 10%, essentially anything reasonable will do. The catch is that if you don't have a solid ML background, you might completely miss that last 10% and never realize!

It's much more satisfying since if you're working on applications, you likely have potential downstream use cases lined up (that's what collaborators are for!). You're also probably the only person working on this specific problem formulation, so you don't need to worry about beating SOTA and squeezing out that last 5% -- your data-driven algorithm is 2x better than a traditional approach, so does it really matter?

Find people to talk to! I definitely agree that the problem with learning by doing in ML is that it would probably be several full time jobs.

What I would suggest (and how I try to get by): find someone -- or several someones -- to discuss ideas with. Instead of learning by doing, learn by discussing how you would hypothetically do something, e.g. solve a certain problem or extend a method to do something else. Your advisor is great for this. If your advisor doesn't have time, try other professors, postdocs, more senior PhD students, or basically anyone who will talk to you.

As for keeping track of the field, my opinion is that there's not actually that much truly new stuff in ML, and everything basically builds on the same themes in different ways. Once you're sufficiently familiar with the general themes, the high level is enough to understand new stuff. I basically never read papers beyond the high level, except if I'm considering using it for my research.