Detecting Wash Sales/Transactions
It is not possible to determine if multiple addresses belong to one wallet, whether it is a deterministic wallet or not.

At best, you can do some form of chain analysis that traces UTXOs back along the chain until you find a common root. For most transactions in a single wallet, there will usually be a convergence point of the coins. However, this is not an exact science, and the results may not be of a high enough confidence to be certain it is happening.

Similarly, you can trace the future spending of the outputs created to see if they converge into a single address. If so, it may indicate the same person was selling/buying items.