If you want to become a research mathematician through self-study, then working through the qualifying exam syllabus for an established math program could be helpful [1].
If you want practical skills in the fields you have listed, then a great way to get them is to work through Gilbert Strang's OCW linear algebra course and Feynman's lectures on physics. That means doing the problem sets, all of them. The former will give you linear algebra, the latter will give you useful analysis/probability/physics. If you diligently solve the P-sets, you will probably be in better shape than 99% of people leaving university with a BS/MS in math/stats/physics.
It is very easy to go down a rabbit hole that is not useful to a practitioner. This is particularly true in analysis and probability theory. Almost no one but a research mathematician needs to know about Lebesgue measures or Radon-Nikodym derivatives or whatever.
[1] https://www.math.harvard.edu/graduate/study-the-qualifying-e...