Is it permissible to combine two jobs simultaneously, one full-time and the other part-time, while prioritizing the first job, with the knowledge of both companies?

It is not permissible for you to combine two jobs during your official working hours without the permission of your employer, because you are a private employee and your benefit is owned by your company during that time. Therefore, you must seek permission from the authorized person, and if they grant you permission, then there is no harm; otherwise, it is not permissible.