The problem is that apparently they don't have this team.

In the face of that reality, a separated internal and external bug trabkin system might be a viable solution.

This would cement an alternate reality, where the growing of the QA team would become more difficult. Trust me, I am talking from experience of recruiting and onboarding hundreds of volunteers into FOSS teams (with varying levels of success and involvement). Recruiting volunteers to FOSS is insanely difficult and any addition of complexity will just result in more headaches.