Hey congratulations on all of those accomplishments! Though with regards to the question, I don't think they are relevant. The following focuses mostly on STEM experiences, but I think applies broadly.
The 20hr work restriction has nothing to do with being an international student. It applies equally to domestic students. The reason, is that 20hrs / week is the minimum requirement to be labeled as a "student", i.e. in order to maintain student status in the eyes of the university and/or government. From what I understand though, this practice differs between private and public institutions. Graduate students live in a strange state between students and faculty. Student status is important for several reasons, like: (1) the university paying for your tuition (2) student benefits like class enrollment and healthcare (3) tax reasons, for both yourself and your institution. You may notice that you pay a suspiciously low tax rate on your earnings.
Over the summer, it's a different story. There is no required time to be in school, meaning that legally, students are free to work >20hrs / week while still maintaining student status. In terms of hours, you can be paid for 40 hrs / week, and indeed like other posters mentioned, often times students plan for this over the course of a year, and will save those earnings to help out during tougher times in the academic year.
So legally, you are free to earn a ton of money over the summer. In practice though, this usually doesn't quite happen for several reasons.
First, your department needs to have funding, which is often a major blocker.
Second, assuming the money is there, your advisor or source of funding needs to agree to pay you for your time. This has both an agreed upon hourly component, as well as agreed upon start and end dates. With regards to advancement to candidacy, most universities have tiered pays, meaning that before advancement you will have an upper bound on your researcher salary. But again, that has nothing to do with hours worked, it's only w.r.t hourly pay. After candidacy, some departments will set standards for payment, while others leave this up to negotiation between students and advisors/department.
Third and finally, there is one additional problem with earning too quickly over the summer, that doesn't apply to everyone. If you were the recipient of a prestigious fellowship, or some other means of earnings, you can go over the annual cap if paid out too quickly (I think the cap starts/ends over the summer). This is not a fun situation to be in, and you basically just lose your money, it doesn't roll over. In this case you may opt for half pay over a longer period of time, even if the working hours were only during a fraction of that time period.
All in all, if you don't feel you're getting the pay you deserve, it's likely a conversation to have with your advisor.
You can also work two jobs over the summer. You can pick up 20hrs / week teaching and 20hrs / week researching. I was only focusing on the initial post, but this is further evidence that there is no working restriction.