I would say that the most serious/compelling physics models are more closely related to the former. But I wouldn’t say phase transition, more like oscillating stuff related to the plasma around the neutron star (eg screening, jiggling plasmoids).

Not for emission. Emission, eg radio emission, comes from plasma. Not from magnetic field. Electric field matters more because it is electric field that accelerates particles. Twisting probably not key effect for emission.

Coincidentally in this talk with Sasha Philippov rn

You mean because there are too many emission models?