Posterior distribution of the derived α_B and α_M (left) and the effective Newtonian coupling μ_∞ and the lensing modification Σ_L, ∞ (right) at three distinct redshifts. Each posterior is derived from the combination of KiDS-Legacy, DESI DR2 BAO, eBOSS DR16 RSD, and Planck 2018 TTTEEE, low-ℓ TT, and low-ℓ EE datasets. The blue contours are inferred with Horndeski gravity modelled by the stable parameter basis ${\widehat{D}}_{\mathrm{kin}}$ and $\mathrm{\Delta }{\widehat{M}}_{\ast }^2$ and the orange contours corresponds to a direct sampling of ${\widehat{\alpha }}_{\mathrm{B}}$ and ${\widehat{\alpha }}_{\mathrm{M}}$ with α_B(a) and α_M(a) proportional to the dark energy density, following Eq. (6). The black dashed lines indicate the GR limit set by α_B = α_M = 0 and μ_∞ = Σ_L, ∞ = 1. Each contour shows the 95% credible interval.