I wrote a post about the statistics of the GRW model and how it should forecast here. Applying it in your case would be a bit more complex. You would use the procedure I outline in that post to construct that latent GRW process for t+h forecast steps of raw_rw, then combine it with all the other time-invariant parts of your model posterior to generate forecasts.
Don’t expect too much from the GRW out of sample.