When sorting buckets by relatedness, JSON "terms" facet must calculate relatedness for every term.
The current implementation uses a standard uninverted approach (either docValues or UnInvertedField) to get facet counts over the domain base docSet, and then uses that initial pass as a pre-filter for a second-pass, inverted approach of fetching docSets for each relevant term (i.e., count > minCount?) and calculating intersection size of those sets with the domain base docSet.
Over high-cardinality fields, the overhead of per-term docSet creation and set intersection operations increases request latency to the point where relatedness sort may not be usable in practice (for my use case, even after applying the patch for SOLR-13108, for a field with ~220k unique terms per core, QTime for high-cardinality domain docSets were, e.g.: cardinality 1816684=9000ms, cardinality 5032902=18000ms).
The attached patch brings the above example QTimes down to a manageable ~300ms and ~250ms respectively. The approach calculates uninverted facet counts over domain base, foreground, and background docSets in parallel in a single pass. This allows us to take advantage of the efficiencies built into the standard uninverted FacetFieldProcessorByArray[DV|UIF]), and avoids the per-term docSet creation and set intersection overhead.