Prior distribution of the effective Newtonian coupling, μ_∞, and the lensing modification, Σ_L, ∞, generated by drawing 500 samples from the prior, given in Table 1. Each line illustrates the evolution of μ_∞ and Σ_L, ∞ as a function of scale factor for one set of parameters generated from the prior. Additionally the coloured lines and shaded regions show the corresponding posterior distribution inferred 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 three rows show the stable basis parametrised by ${\widehat{D}}_{\mathrm{kin}}$ and $\mathrm{\Delta }{\widehat{M}}_{\ast }^2$, the direct sampling of ${\widehat{\alpha }}_{\mathrm{B}}$ and ${\widehat{\alpha }}_{\mathrm{M}}$, and the stable basis parametrised by ${\widehat{D}}_{\mathrm{kin}}$ and ${\widehat{c}}_{\mathrm{s}}^2$, respectively.