Vanishing of first Betti numbers for trialitarian groups

Let $G$ be a semisimple algebraic group over ${\mathbb Q}$ obtained by restriction of scalars from a group of type ${}^3D_4$ or ${}^6D_4$ over a totally real number field, and suppose that $G^{\rm nc}=O(7,1)^0$. For every congruence subgroup $\Gamma\subset G({\mathbb Q})$, write $b_1(\Gamma)$ for its first Betti number. First-Betti-number vanishing conjecture. One has

$$b_1(\Gamma)=0.$$

The source derives this assertion from its conjectural automorphic functoriality statement; it is therefore presented as an open consequence rather than an unconditional theorem.