Up to an orthogonal change of variable you may assume $U = \begin{bmatrix}I_d\\0\end{bmatrix}$. In this basis, the problem becomes $$ \min_{X_{11} \succeq 0} \left\|\begin{bmatrix}X_{11} & X_{12}\\ X_{12}^T & X_{22}\end{bmatrix} -\begin{bmatrix} M_{11} & M_{12}\\M_{12}^T & M_{22}\end{bmatrix} \right\|_F, $$ which clearly has solution $X_{12}=0$, $X_{22}=0$ and $X_{11} = M_{11}^*$ (where $M_{11}^*$ is defined as in your text, i.e., $M_{11}^*=V\max(D,0)V^{-1}$ with $M_{11}=VDV^{-1}$), .

Up to an orthogonal change of basis you may assume $U = \begin{bmatrix}I_d\\0\end{bmatrix}$. In this basis, the problem becomes $$ \min_{X_{11} \succeq 0} \left\|\begin{bmatrix}X_{11} & X_{12}\\ X_{12}^T & X_{22}\end{bmatrix} -\begin{bmatrix} M_{11} & M_{12}\\M_{12}^T & M_{22}\end{bmatrix} \right\|_F, $$ which clearly has solution $X_{12}=M_{12}$, $X_{22}=M_{22}$ and $X_{11} = M_{11}^*$ (where $M_{11}^*$ is defined as in your text, i.e., $M_{11}^*=Q\max(D,0)Q^{-1}$ from the eigendecomposition $M_{11}=QDQ^{-1}$).