COS VII presents a forecast-level analysis of the observational sensitivity of future cosmological surveys to late-time growth-sector deformations within the CoreLumen framework. The study models the observational response of representative DESI-like spectroscopic surveys together with Euclid-like and LSST-like weak-lensing surveys using a transparent Fisher-matrix forecast framework. The late-time growth modification is parameterized through a phenomenological deformation µ(a) = 1 + µ0 ΩDE(a), where the parameter µ0 quantifies deviations from standard ΛCDM growth. The analysis shows that while DESI-like probes alone provide weak direct sensitivity to the deformation amplitude, Euclid-like and LSST-like lensing surveys significantly tighten the constraint. The combined survey forecast reaches σ(µ0) ≈ 0.07. Compared to a representative present-day benchmark σpresent(µ0) ≈ 0.30, this corresponds to an improvement factor of approximately 4.3. This work provides the forecast bridge between current observational constraints and the future reconstruction of the growth sector addressed in the subsequent COS VIII analysis.