“Physics is broken! Matter is an illusion, the atom is just trapped light!”
Wrong. Light and matter are not the same thing. Light has no mass, while the tiny pieces that build atoms do. You cannot make solid matter simply by trapping beams of light.
Show the working
Matter particles (fermions) and light particles (photons) belong to fundamentally different classes in the Standard Model. Photons are massless spin-1 gauge bosons with rest mass m_0 = 0. Leptons (like electrons, m_e ~ 0.511 MeV/c^2) have non-zero invariant rest mass acquired through Yukawa coupling to the Higgs field vacuum expectation value (v ~ 246 GeV). Nucleons (protons and neutrons) derive ~99% of their ~938 MeV/c^2 rest mass from Quantum Chromodynamics (QCD) binding energy, quark kinetic energy, and gluon field energy via E = mc^2. Furthermore, matter obeys Fermi-Dirac statistics and the Pauli exclusion principle, which prevents atomic collapse and gives matter volume, whereas photons obey Bose-Einstein statistics. Trapping light cannot generate conserved fermion quantum numbers (such as lepton number or baryon number) without violating fundamental conservation laws.
Where this comes from: Particle Data Group Standard Model review and QCD lattice calculations.