 Longitudinal capacitor field under a normal boost

For ideal oppositely charged parallel plates, the normal electric field is $\sigma /{ϵ}_0$. A boost along that normal leaves each transverse plate area unchanged. Invariance of total charge therefore preserves surface charge density and the normal electric field. The plate separation contracts, but the large-plate field does not depend on that separation. Including longitudinal contraction in a voltage argument while holding voltage fixed would impose an unsupported extra assumption.