functional analysis and differential geometry are very very important
functional analysis is the math behind quantum mechanics. differential geometry is the math behind relativity.
algebraic topology is not that important but it's useful for differential topology/geometry and anything with manifolds. i wouldn't prioritize it but it's fun.
galois theory sounds worthless to what you're doing, but you should do things which interest you.
i would recommend looking into proper PDE theory and dynamical systems theory after doing some measure theoretic real analysis and some functional analysis. ideas like distribution theory, ergodicity, and unbounded (differential) operators on hilbert spaces are really central to much of mathematical physics. DEs at this level are not "lol solve le equation," it's much more like normal analysis.