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Here is a notebook doing something similar (checking HMC results are suitable) for a project I'm working on. The bayesplot R package is pretty good for this. Perhaps there is a Python equivalent.
Recent idea I've borrowed for this is to take the parameter with the lowest ESS or highest R hat or and present the traceplot for that. If even for the worst parameters they look OK then you should be fine for the others (I think this is reasonable in an academic context when a reviewer would want to know they look reasonable but doesnt want to look at 100s of traceplots, maybe less utility outside a paper context).
Stan produces some information about the mixing and rejection rate of the markov chain. We should plot this as part of our model checking.
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