Emergent Gravity from String Field Theory III: Cosmological Phenomenology, Vacuum Friction, and Tension Resolution

The standard cosmological model (CDM) successfully describes the large-scale universe but fundamentally lacks a microphysical derivation for the gravitational constant (GN) and the dark energy density (), while increasingly facing severe observational tensions in the Hubble parameter (H₀) and the structure growth amplitude (S₈). Building upon the non-perturbative phase-space stability and ghost-free de Rham-Gabadadze-Tolley (dRGT) massive gravity structure derived ab initio in Papers I and II of this series, we demonstrate that cosmic expansion emerges as a thermodynamic consequence of the fundamental String Field Theory (SFT) vacuum condensate. This top-down framework allows us to translate rigid microscopic SFT invariants into falsifiable macroscopic cosmological predictions without phenomenological fine-tuning. We demonstrate that the fundamental macroscopic gauge coupling (g₅ 0. 653) required to stabilize the string lattice generates an extreme local vacuum rigidity. This massive geometric stiffness dynamically triggers an Active Screening Architecture---incorporating the non-linear Vainshtein mechanism and Geometric Dark Confinement---safely decoupling anomalous scalar and vector degrees of freedom to rigorously recover General Relativity within the Solar System. On cosmological scales, however, the continuous interaction between matter and the background lattice drives a non-conservative Topological Volume Generation. By strictly applying the geometric scaling invariant of the transverse string worldsheet (ₓ₇ = 1/24) and the macroscopic lattice percolation threshold (pc 0. 1891), we analytically predict a late-time dynamic phantom dark energy epoch (w₀ = -1. 08). Crucially, this topological space-creation exerts a macroscopic vacuum phase-space drag on massive bodies, yielding a precise, parameter-free prediction for the dynamic suppression of linear structure growth: f₈ -1. 7151\%. Comprehensive parameter-free Bayesian MCMC inference (incorporating Planck 2018, KiDS-1000, DESI, and Pantheon+ datasets) demonstrates that this specific "Phantom-Suppression" signature simultaneously resolves the persistent H₀ and S₈ cosmological tensions. The analysis yields decisive statistical evidence (2 B = +16. 8) favoring the SFT Emergent Framework over the standard CDM baseline, establishing the non-perturbative string vacuum not merely as a mathematical curiosity, but as a highly competitive, observationally preferred cosmological paradigm.