  We study holographic entanglement entropy and holographic complexity in a
two-charge, $\frac{1}{4}$-BPS family of solutions of type IIB supergravity,
controlled by one dimensionless parameter. All the geometries in this family
are asymptotically AdS$_3 \times \mathbb{S}^3 \times \mathbb{T}^4$ and, varying
the parameter that controls them, they interpolates between the global AdS$_3
\times \mathbb{S}^3 \times \mathbb{T}^4$ and the massless BTZ$_3 \times
\mathbb{S}^3 \times \mathbb{T}^4$ geometry. Due to AdS/CFT duality, these
geometries are dual to pure CFT heavy states.
  We find that there is no emergence of entanglement shadow for all the values
of the parameter and we discuss the relation with the massless BTZ result,
underlying the relevance of the nature of the dual states.
  We also compute the holographic complexity of formation of these geometries,
finding a nice monotonic function that interpolates between the pure AdS$_3$
result and the massless BTZ one.
