Hi,
I am not sure how much are the simulated data representative of your actual data, but categorical models in general expect there to be some variability in the response given predictors. (This is similar to your other inquiry at Multilevel ordinal model - large values in threshold and group level sd estimates?) In the data you’ve shown the group seems to completely determine Y. I think in frequentist context, one would speak about “complete separation” (and freqeuntist models will fail as the maximum likelihood estimate for the group effect will be infinite). Bayesian models do not fail so badly in face of complete separation, because the prior let’s us avoid the infinity in the estimates, but still, the data + prior are unable to inform the coefficients beyond putting a lower/upper bound. Also prior has a big influence on the final values of the coefficients in this case.
Also note that in a categorical model, the coefficients are always relative to the reference category, so you cannot avoid estimating a value for all categories to determine a distribution for the outcome, so I don’t think removing the coefficients would make much sense - if you really wanted to do it, I think you’d need to go to pure Stan.
Best of luck with your model!