  We study the cosmic microwave background (CMB) radiation in the unified
description of the effective field theory (EFT) of dark energy that
accommodates both scalar-tensor and vector-tensor theories. The boundaries of
different classes of theories are universally parameterised by a new EFT
parameter $\alpha_V$ characterising the vectorial nature of dark energy and a
set of consistency relations associated with the global/local shift symmetry.
After implementing the equations of motion in a Boltzmann code, as a
demonstration, we compute the CMB power spectrum based on the $w$CDM background
with the EFT parameterisation of perturbations and a concrete
Horndeski/generalised Proca theory. We show that the vectorial nature
generically prevents modifications of gravity in the CMB spectrum. On the other
hand, while the shift symmetry is less significant in the perturbation
equations unless the background is close to the $\Lambda$CDM, it requires that
the effective equation of state of dark energy is in the phantom region $w_{\rm
DE}<-1$. The latter is particularly interesting in light of the latest result
of the DESI+CMB combination as the observational verification of $w_{\rm
DE}>-1$ can rule out shift-symmetric theories including vector-tensor theories
in one shot.
