SCS and Mosek give very different answers

I don’t think it’s obvious that this is a bug in SCS. It’s returned a solution that it determined satisfies the KKT conditions for your problem according to its own internal tolerances. There’s no particular reason to think that that hasn’t worked, it’s just that those tolerances are not very tight relative to the interior point solvers you are comparing against.

That said, I tried this problem with Mosek, SCS, Clarabel and COSMO and got 4 different answers for the optimal objective value (NB: you must use a consistent seed value in the random number generation to make this comparison, but they still come out different).

Worth noting also that the norms of both the primal and dual optimizers are really big : ~5e6 for the primal and ~3e5 for the dual (in Clarabel at least). Maybe therefore not that surprising that the different results for the objective value vary a bit between solvers.