Joint scaling limit of the spanning-tree Peano curve and area measure

In the setting of the spanning-tree LQG scaling-limit conjecture, let $\lambda^{\infty,n}$ be the image in $\mathbb C$ of the Peano curve $\lambda^\infty$ of $T^\infty$ under the uniformization map. Let $\eta$ be a whole-plane $\operatorname{SLE}_8$ from $\infty$ to $\infty$, independent of $\mu_{\mathsf h}$. View both curves modulo monotone reparametrizations. The joint Peano-curve scaling-limit conjecture. The pair $(\mu^n,\lambda^{\infty,n})$ converges jointly in law to $(\mu_{\mathsf h},\eta)$ modulo rotations. This is the curve-decorated refinement of the preceding LQG scaling-limit conjecture, identifying the limiting Peano curve as whole-plane $\operatorname{SLE}_8$ independent of the limiting quantum area measure.