Note that being divisible, a.k.a. strongly collectionwise normal, is equivalent to every open cover being uniform, that is, every open cover has a refinement such that if two points are connected by a chain of two sets in the refinement with non-empty intersection (e.g. there are points $x,y,z$ w...

Completely revised. In The cometrizability of generalized metric spaces, Section $4$, Taras Banakh and Yaryna Stelmakh construct a regular topology $\tau$ of weight $\omega_1$ on $\Bbb Q$ such that $\langle\Bbb Q,\tau\rangle$ is not cometrizable and hence not stratifiable. (I have not yet gone th...