You should be able to pass more parameters to your simulator, even if they are constants. Try wrapping them in pytensor.tensor.as_tensor() if you are getting errors.
sum_stat should be a function that summarizes the observed data and the one returned from the simulator. The distance function is then computed on the two summaries (and scaled by epsilon) to define the simulator likelihood.
It may make things easier for debugging to simply return the mean/std from your simulator, and also pass the mean/std as the observations. Then you can set sum_stat = "identity", since there’s no further processing to do