I am a shareholder in some companies. That does not give me any right to personal information about employees or ex-employees.
The charter does NOT say that the BBC is accountable to licence payers. It does require the BBC to observe high standards of openness and seek to maximise transparency and accountability. However, the BBC is not exempt from GDPR. Making a public announcement about the nature of the allegations against Mills is likely to be a breach of GDPR. That doesn't mean we won't find out, but thinking there is some kind of duty on the BBC to tell us is simply wrong. As far as the law is concerned, they are more likely to be under a duty to keep the information confidential.