Let $(X_i)_{i=1}^N$ be mean zero sub-Gaussian random vectors in $\mathbb{R}^n$, i.e., there exists $C>0$ such that for all $u\in \mathbb{R}^n$, $$ \mathbb{E}\left[e^{u^\top X_i}\right]\le e^{\frac{C^2}{2}|u|^2}, \forall i=1,\ldots, N. $$ Let $(A_i)_{i=1}^N\subset \mathbb{R}^{n\times n}$ be given matrices. I was wondering whether there exists a concentration inequality for the quadratic term $$ \left\langle \sum_{i=1}^N A_i X_i,\sum_{i=1}^N A_i X_i\right\rangle, $$ with a precise dependence on the coefficients $(A_i)_{i=1}^n\subset \mathbb{R}^{n\times n}$?
In other words, I am looking for a multidimensional extension of Hanson-Wright inequality (see here) with matrix coefficients. I would appreciate it if you could provide any relevant references on the topic.