Hmmm using these parameter you will get pretty weird prior where there is low probability almost everywhere. As:
mu = 0.02099537805606402
sd = 1.179636714844027e-06
alpha = mu**2 / sd**2
beta = mu / sd**2
alpha, beta
(316774953.93371433, 15087842337.862612)
You should check your Gamma prior and use alpha/beta parameterization.
As for the identical samples, you can hardly tell anything from 5 samples. Usually after tuning (ie, the sampler is in the typical set and the step size etc are well tuned) and your problem is well post (no high curvature places), samples are almost always different using NUTS. But if either of above is not satisfied you will see these kinds of stuck chain.