In NIST MLDSA specs supplying external mu is allowed instead of computing it internally in the API.
Algorithm 8 ML-DSA.Verify_internal(ππ, π β², π) . . . 7: π β (H(BytesToBits(π‘π)||π β², 64)) β· message representative that may optionally be computed in a different cryptographic module
This is useful in base data the needs to be signed/verified is scattered so supplying it in one continuous memory location can be a problem on memory constrained devices