Hello !
The seeding values (𝜌, 𝜎) are incorrect. Based on the FIPS 203 - Algo 13 - Line 1, they are supposed to be the concatenation of d and k (resulting in 33 bytes ), then hashed through SHA3-512.
The current (𝜌, 𝜎) are the result of only the hashing of d, without any concatenation with k.