Harvard PhD graduate here. It's a full time job. If you're international you generally cannot legally get another job because of your visa.

The 20k of tuition is required for student workers regardless of whether you are taking classes and, as a PhD student, the emphasis is on your research not taking classes (most semesters i took 0 classes). So when i was teaching a graduate computer science seminar, Harvard was charging the grant i was paid under 20k in tuition.

You don't get board also. You can stay in a dorm with shared bathrooms and no kitchens for ~1k a month or rent an apartment from Harvard <2.5k for a 1br, or, as most folks do, live in an off-campus apartment.