  Recently, in [1], we presented the first combined non-parametric
reconstruction of the three time-dependent functions that capture departures
from the standard cosmological model, $\Lambda$CDM, in the expansion history
and gravitational effects on matter and light from the currently available
combination of the background and large scale structure data. The
reconstruction was performed with and without a theory-informed prior, built on
the general Horndeski class of scalar-tensor theories, that correlates the
three functions. In this work, we perform a decomposition of the prior and
posterior covariances of the three functions to determine the structure of the
modes that are constrained by the data relative to the Horndeski prior. We find
that the combination of all data can constrain 15 combined eigenmodes of the
three functions with respect to the prior. We examine and interpret their
features in view of the well-known tensions between datasets within the
$\Lambda$CDM model. We also assess the bias introduced by the simplistic
parameterizations commonly used in the literature for constraining deviations
from GR on cosmological scales.
