I don’t quite understand why you are adding sigma here in the first place. You already have a standard deviation parameter by design of the model (class sd) and now you are adding yet another one on top (sigma) that is only informed by this 1 standard deviation parameter. This cannot go well. What you did was not to set a normal or student t prior on the random effects but a (half) normal or student t prior on their SD with yet another hyperparameter. If you really want to use a student-t random effects you drop your prior statements and speciy in the formula y ~ (1 | gr(x_1, dist = "student")). Please note that this feature is experimental, not documented and not officially supported.
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