What is the ruling on leaving work before the official end of working hours with the manager's knowledge, and the work not being public-facing, due to the employer's denial of the employee's rights and not recognizing their advanced academic degree, which has affected their salary?

The fact that the employer did not accredit the academic certificate does not justify non-compliance with official working hours, even if the work is completed, because the employment contract is tied to a specific time and specific tasks. There is no harm in an emergency departure with the permission of the manager if it does not disrupt work. As for the certificate, either it is not accredited due to its specialization or the issuing authority, which is not an issue, or it conforms to what they have, in which case one should try to get it accredited through legitimate means.