arXiv:2611.13303v1 Announce Type: new Abstract: In this paper we develop a second-order, fully decoupled, non-iterative partitioned method for the time-dependent Stokes--Biot problem on fixed domains. In previous work \cite{WangLeeCanic2026SecondOrder}, a Robin--Robin scheme with these features was introduced, and its stability and error estimates were established under the sufficient parabolic CFL-type condition $\Delta t\lesssim C_*h^2$. The main improvement of the new scheme is weakening the CFL-type condition to a linear CFL-type condition $\Delta t \lesssim C_*h$. This can be achieved with a new splitting approach by replacing the poroelastic mechanical normal Robin condition by its physical Neumann-type traction condition, which results in a Neumann--Robin splitting. For fixed coefficients satisfying the stated assumptions, we prove a fully discrete energy bound under a restriction of $\Delta t\lesssim C_*h$. The improvement over the parabolic restriction in the earlier Robin--Robin analysis follows from eliminating the interface residual that requires two inverse-trace estimates. We also establish an energy-norm error bound of order $h^k+\Delta t^2$ under explicit regularity, finite element approximation, and initialization assumptions. Numerical experiments with manufactured solutions examine spatial and temporal accuracy and compare the Neumann--Robin and Robin--Robin schemes. A 3D cylindrical pressure-pulse benchmark further investigates their numerical stability behavior. The results distinguish the less restrictive sufficient stability condition established analytically from the observed stability thresholds of the two schemes.