Two photons "annihilating" to two photons is... well.. photon-photon scattering, but you can also produce other particles. High energy gamma rays pair produce

Two photons "annihilating" to two photons is... well.. photon-photon scattering, but you can also produce other particles. High energy gamma rays pair produce into electron positron pairs with the cosmic microwave background, so at high enough energies, they don't go very far through the universe. https://en.wikipedia.org/wiki/Two-photon_physics https://en.wikipedia.org/wiki/Two-photon_physics