Apply LLM-generated labels to the supplied clusters in place. On any failure (prompt missing, LLM error, parse error) the clusters are left untouched and the method resolves without throwing.
Cluster summaries to label (mutated in place).
Projected points, used to sample member labels per cluster.
OptionalcontextUser: UserInfoUser context for prompt execution (required server-side).
Optional override of the naming prompt name.
Generates human-readable labels for clusters using an LLM.