Expectation w.r.t. Haar measure of $R\cdot\text{diag}(R^\top \Sigma R) \cdot R^\top$

Question

Let $\Sigma \in \mathbb{R}^{n \times n}$ be a positive definite matrix and $\mu$ be the Haar measure over all orthogonal matrices $\in \mathbb{R}^{n\times n}$.
What is $$\mathbb{E}_{R \sim \mu} \left[R\cdot\textrm{diag}(R^\top \Sigma R) \cdot R^\top\right]?$$