Quick summary note here from a discussion with WMDE folks, and ahead of us have a specific task from the front-end component:

There are components that WMDE own for doing Wikidata Entity / Lexeme selectors, BUT the main ones on Wikidata.org are still jQuery UI and not usable, and the Vue ones that exist aren't yet based on Codex.
The back-end query for Lexemes we can use is: …api.php?format=json&formatversion=2&action=wbsearchentities&type=lexeme&language=foo&search=bar — example
There's an example in the Codex documentation of how to configure the CdxLookup component (which we already use in WikiLambda) to fetch Wikidata entities with infinite scroll

A quick note as discussed with Denny that our custom Types for this will need to have special handling – in the orchestrator (special dereferencing, including the new L1234-S1 format), in the front-end (custom selector and renderers), and perhaps elsewhere – and so should be pre-defined Objects rather than created on-wiki.