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The first problem arises because the domain of ginv is M and not U (since g is defined as g = M.riemannian_metric('g')) and the default frame of M is Rho.frame(). So, you should set:

sage: M.set_default_frame(Tau.frame())

The second problem lies in the definition of psi:

sage: psi = U.scalar_field({Rho: function('Psi')(u1,u2,u3)}, name='psi',latex_name='\Psi')

You are declaring the coordinate expression of psi in the chart Rho, but (u1,u2,u3) are coordinates of the chart Tau, so that function('Psi')(u1,u2,u3) appears as a constant function. For instance, one has diff(function('Psi')(u1,u2,u3), r12) = 0. Hence the Laplace-Beltrami operator applied to psi yields zero.