So this is specific exemptions approved by the CAA based on individual programmes submitted by larger residential schools, rather than a general resumption?
Yes. And it's very limited at present.
I don't believe the CAA stopped training - the decision to voluntarily suspend training activity was made by training organisations. My understanding is that the resumption of commercial training has been permitted by the DfT and that any exemptions have been granted higher up to enable specific non-civilian contracts held by commercial providers to continue during the last lockdown phase. A general resumption of commercial training and associated ratings is permitted now in any case.