A direct calculation shows the geometric braid action on Fukaya-Seidel categories of Coulomb branches agrees with Webster's combinatorial action, so Aganagic's invariant is Khovanov homology over the integers.
Towards a mathematical definition of Coulomb branches of 3-dimensional n=4 gauge theories, II.Advances in Theoret- ical and Mathematical Physics, 22(5):1071–1147, 2018
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Aganagic's invariant is Khovanov homology
A direct calculation shows the geometric braid action on Fukaya-Seidel categories of Coulomb branches agrees with Webster's combinatorial action, so Aganagic's invariant is Khovanov homology over the integers.