Adaptive step size and NUTS

I am wondering what is the correct way to use samplers with adaptive step size with NUTS as the base sampler. The STS model notebook provides an example of such usage, but it seems to work in an undesired manner. For example, although the desired approximate acceptance rate is set to 0.75, during the sampling it is very close to 1. I tried to run longer adaptation/sampling, as well as several my own models with similar code for adaptation and it seems that at least DualAveragingStepSizeAdaptation severely underestimates the optimal leapfrog integration step size during the adaptation phase. With HMC sampler such misbehaviour does not manifest, so I suspect that the reason is that the NUTSKernelResults.log_accept_ratio quantity is not the one we need to pass for the log_accept_prob_getter_fn of DualAveragingStepSizeAdaptation. I tried to browse through the source codes to figure out what exactly is returned in NUTSKernelResults.log_accept_ratio, but this turned out quite challenging.

Could you please advice on what would be the correct way to adapt step size in NUTS?

Start with the STS approximate-inference notebook and trace how DualAveragingStepSizeAdaptation receives NUTSKernelResults.log_accept_ratio through log_accept_prob_getter_fn. Compare that path with the HMC sampler and inspect the relevant NUTS and adaptation source. Done means determining whether the reported acceptance quantity is appropriate and documenting or correcting the supported adaptation usage.