Strong Ramanujan bound for traces of Hecke operators on Drinfeld cusp forms

Let $A=\mathbb{F}_q[T]$, let $\mathfrak p\trianglelefteq A$ be a maximal ideal of degree $d$, and let $n\geq 1$. For integers $k,l$, write $\mathbf{T}_{\mathfrak p}$ for the corresponding Hecke operator on the Drinfeld cusp-form space $\mathrm{S}_{k,l}$. Strong Ramanujan bound. One has

$$\deg \operatorname{Tr}\left(\mathbf{T}_{\mathfrak p}^n\mid\operatorname{S}_{k,l}\right)\leq \frac{nd\left(k-(q+1)\right)}{2}.$$

This is presented as a strong form of the Ramanujan bound for Drinfeld modular forms. The source gives no resolution status, so the assertion remains open in this database.