wbsearchentities used to return label, description, and (if matched) aliases in the requested search language (or fallback language of that). This chanegd with T90692, which introduced an internal search interface that would provide the matched term in the search language (or one its fallback languages) and display terms (a label and a description) in the user language (or one of its fallback languages).
wbsearchentities will currently return the label and description in the user language, and the (single) matched term in the "aliases" slot, as plain strings. In addition, wbsearchentities now returns a "matched" field with the matched term as a full term structure.
We should add a "display" field, which would contain the full term structures (including the actual language) of the label and description. The old label, description, and alias fields should be deprecated. The Wikibase UI should be changed to only use the "matched" and "display" fields.