Are you looking for something like a factor analysis?
Or do you directly want to cluster features using rows of the correlation matrix? In that case perhaps terms like Hierarchical Clustering, Blockmodeling could be helpful to get started.
There are apparently Bayesian versions of hierarchical clustering if you want to do it in the Bayesian framework (don’t have experience with these though so don’t know how involved they are):
There is a clustering method called Gaussian Mixture Models which can be done in the Bayesian framework, you can try to apply that to the rows of your matrix too (but people seem to be using hierarchical clustering for this question more often).
ps: If you decide to go down the Bayesian clustering pathway, the links below could be helpful in understanding some of the technicalities involved in Bayesian clustering: