You may want to read the following regarding technicalities involved in Gaussian Mixture Models within Bayesian framework:
https://mc-stan.org/docs/2_27/stan-users-guide/mixture-modeling-chapter.html
If your model diverged but still ran to completion, you can look at trace plots to see whether if what you are experiencing is a mixing problem. Some advised tricks of the trade are using Multivariate Normals if in higher dimensions, using ordering transformation on one of the coordinates, supplying initial conditions to your priors, using ‘advi+adapt_diag’ initialization. If these don’t remedy the mixing, you may need to restrict your priors or choose a coordinate system where ordering priors becomes more natural (for instance if you are in 2D and you can not really order your clusters based on x or y but each cluster seems to have different radius from some centre point then you may want to formulate the question in polar coordinates etc).