Traveling to Puerto Rico with expired visa but valid status

I think this question was asked before¹ on another post, but I feel paranoid and want to hear some opinions on my unique situation.

I came to the USA on a tourist visa 18 years ago and have never been out since. Thus my visa has long expired and since then I have changed my status to F1 status without leaving the States (so I do not have an F1 visa, just the status).

I am now into my fourth year of PhD and my advisor wishes me to present some works I have published at a conference held in Puerto Rico.

I have heard that if I ever visit another country, then re-entry would be impossible as my visa expired. This would mean having to go back to South Korea (legally speaking, I am a South Korean citizen) and applying for a visa to enter the States again. This would probably be impossible since I have left the country with a tourist visa and never returned since and did not serve in Korea's mandatory military service.

If I get deported during this critical time of my career, it would be disastrous, so I wish to take utmost caution when I travel out of the 50 states. Will I be able to travel to Puerto Rico without running any risk of getting deported, provided I have valid I-20 and I-94?

¹It's not exactly a duplicate because it doesn’t mention returning.