  $\require{mhchem}$The square-kagome lattice Heisenberg antiferromagnet is a
highly frustrated Hamiltonian whose material realizations have been scarce. We
theoretically investigate the recently synthesized $\ce{Na6Cu7BiO4(PO4)4Cl3}$
where a Cu$^{2+}$ spin-$1/2$ square-kagome lattice (with six site unit cell) is
decorated by a seventh magnetic site alternatingly above and below the layers.
The material does not show any sign of long-range magnetic order down to 50 mK
despite a Curie-Weiss temperature of $-212$ K indicating a quantum paramagnetic
phase. Our DFT energy mapping elicits a purely antiferromagnetic Hamiltonian
that features longer range exchange interactions beyond the pure square-kagome
model and, importantly, we find the seventh site to be strongly coupled to the
plane. We combine two variational Monte Carlo approaches,
pseudo-fermion/Majorana functional renormalization group and Schwinger-Boson
mean field calculations to show that the complex Hamiltonian of
$\ce{Na6Cu7BiO4(PO4)4Cl3}$ still features a nonmagnetic ground state. We
explain how the seventh Cu$^{2+}$ site actually aids the stabilization of the
disordered state. We predict static and dynamic spin structure factors to guide
future neutron scattering experiments.
