A little trick and has been addressed
I don’t see where the problem specification you provided includes the constraint of Y being semidefinite; Whether it should be so-constrained is your responsibility.
I’m not sure what the constraint on the 2nd to last line is, but perhaps P_{\beta_\tau^*}Y == 0, although I have no idea what P_{\beta_\tau^*} means, and perhaps this is toitally wrong.
You haven’t provided a reproducible problem, because the input data is not provided. You should at least show the solver and CVX output.
Beyond that, all of https://yalmip.github.io/debugginginfeasible/ is applicable to CVX, except for section 1.