Looks like it could be just a difference in the volatility priors (I suspect coming mostly from the mu of the GaussianRW).
Your v_cap seems to be around 1/0.1=10, which is twice as large as the one in their model. On the other hand, I am not sure if the concentration should map to 1/sigma or 1/ sigma**2. If it’s the later your average would be roughly equivalent to sqrt(1/0.1)=3.16 which looks to be be on the same ballpark as the plot.
Edit: Looking at the raw data, I think your results look more “sensible”