Question for Late[st] and Late[cl-r]

[LaneBoyGoner]

Late[st] is currently on sale for $14.99 on the ps store while [cl-r] isn’t. Will I be able to get [cl-r] just by purchasing [st]? I have read somewhere that the trophy list for [cl-r] will only appear if you bought the digital version of [st], as I have purchased a physical copy of [st] last time but got confused over the versions. Although it did have a [cl-r] update on history log, no new list had appeared. So would it be better to buy [st] digital to get ahold of [cl-r] list, or do I have to buy [cl-r] separately?