Just had the same problem and found that if I replace "req.pipe(busboy)" with "busboy.end(req.rawBody)" it works.
Seems in Firebase Functions, req is already fully parsed, and the stream is closed, so req.pipe(busboy) won’t work and causes “Unexpected end of form.”
Instead, use busboy.end(req.rawBody) to feed the buffered body directly to Busboy. This works because Firebase makes the full raw body available via req.rawBody.