AgglomerativeClustering.n_components_ is the number of connected components in the graph. That's a bit confusing since n_components_ has a very specific meaning in other places in sklearn.
In particular, FeatureAgglomeration inherits this n_components_, so this is a transformer that as n_components_ which doesn't correspond to the output dimensions.
If we explicitly store the output dimension, that might be less of an issue, but I find the naming is a bit misleading and maybe we could use n_connected_components_ instead?