There is a bug in the way that pyfixest parses formulas. It's illustrated simply with this code:

You can see I vary the categorical variable, but the prediction stays the same. This is because pyfixest parses the string formula from scratch in the predict method with the newdata dataframe. I have drafted a PR that addresses this by storing the formulaic modelspec object and re-using that for creating the model matrix when doing out of sample predictions: #839