It’s a bit of both. Cbc is the MIP solver. It uses the LP solver Clp to solve the LP subproblems. But there is no API in Cbc to query the dual value found by Clp.
Regardless though, you should not use Cbc.jl or Clp.jl with SDDP.jl. The way that the Julia wrappers are structured mean that they will not be efficient. Just use HiGHS instead.