there should be a convenience method in Wikibase lua that gives the ItemId of the connected page. This can be simple as exposing the getEntityIdForCurrentPage method in mw.wikibase.lua. This method gets the id via SiteLinkLookup which is efficient.

Right now, for example on enwiki, they have such a method but it requires loading the entity object just to get the id, which is not so efficient.

https://en.wikipedia.org/wiki/Module:Wikibase

PS. for the methods in the module that get the label and site link, I think fetching the entity id is not necessary since mw.wikibase.label and mw.wikibase.sitelink internally do that automatically (via SiteLinkLookup) if id is not provided as an argument.