Hello,
Have you tried some troubleshooting steps like removing the intercept or removing every other term except intercept and B etc. Given that it is only the intercept and w that have large standard deviations when together but not intercept on its own, maybe there some sort of identifiability problem where the expressions containing these parameters end up having similar contributions. What does B look like? An actually fully working code would make it easier to diagnose the problem. You could also use az.plot_pair to see if intercept and w are correlated etc.