Addendum to the ISTG Trilogy: Phenomenological Tests and Observational Prospects — Relativistic Tests with Binary Pulsars, Strong Lensing in Galaxy Clusters, and Signatures for the Next Generation of Detectors

This essay constitutes the integrative and phenomenological Addendum to the foundational trilogy on Informational Scalar-Tensor Gravity (ISTG). Its purpose is to confront the effective theory with astrophysical and cosmological observables that provide particularly stringent tests of departures from General Relativity. The work considers scalar dipole radiation in binary pulsars, strong gravitational lensing in galaxy clusters, the scale-dependent growth of cosmological structure, and gravitational-wave propagation. Particular attention is given to the environmental screening mechanism proposed within ISTG and to the possibility that the informational scalar field may contribute to effective gravitational potentials across different physical scales. The observational signatures are formulated as quantitative tests rather than as established confirmations. The Addendum develops phenomenological parametrizations for compact-object screening, cluster-scale lensing, cosmological perturbations, and gravitational-wave propagation, together with a preliminary Python implementation intended as a computational scaffold for future numerical investigations. A central methodological requirement is that the same underlying parameter set must be confronted with constraints arising from Solar-System tests, binary pulsars, galaxies, galaxy clusters, cosmological structure formation, and gravitational-wave observations. The framework is therefore presented as a falsifiable phenomenological programme rather than as an empirically validated theory. The present work does not claim that the proposed mechanisms have already reproduced the relevant observational datasets. Instead, it identifies the equations, parameters, numerical calculations, and observational comparisons required to determine whether Informational Scalar-Tensor Gravity can remain viable across multiple physical scales. The Addendum concludes that the next stage of the ISTG programme is numerical: deriving the complete perturbation equations, determining the allowed parameter space, solving compact-object and cluster configurations, and confronting the resulting observables with public astrophysical data.