What seems to have worked is just call
await Zotero.initializationPromise
await Zotero.Translators.init()
and not doing any of BBTs initialization until they both resolve. I had so far only awaited Zotero.initializationPromise, and awaited Zotero.Translators.init() mid-startaup when I was installing the translators. This also seems to have taken care of the connector problem.