  We study the entanglement entropy of Hamiltonian SU(2) lattice gauge theory
in $2+1$ dimensions on linear plaquette chains and show that the entanglement
entropies of both ground and excited states follow Page curves. The transition
of the subsystem size dependence of the entanglement entropy from the area law
for the ground state to the volume law for highly excited states is found to be
described by a universal crossover function. Quantum many-body scars in the
middle of the spectrum, which are present in the electric flux truncated
Hilbert space, where the gauge theory can be mapped onto an Ising model,
disappear when higher electric field representations are included in the
Hilbert space basis. This suggests the continuum $(2+1)$-dimensional SU(2)
gauge theory does not have such scarred states.
