Constraints on α_B (left) and α_M (right) as a function of scale factor for 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 contour results from the analysis with Horndeski gravity modelled by the stable parameter basis ${\widehat{D}}_{\mathrm{kin}}$ and $\mathrm{\Delta }{\widehat{M}}_{\ast }^2$ and the orange contour 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 green contour shows the derived constraint on α_B when sampling ${\widehat{D}}_{\mathrm{kin}}$ and ${\widehat{c}}_{\mathrm{s}}^2$ for a fixed Planck mass and therefore imposing α_M = 0. The solid line shows the mean of the posterior and the shaded region illustrates the 68% credible interval. The prior distributions of α_B and α_M for each model are displayed in Fig. C.1.