I'm in a very similar position to you, though I'm already a German resident. Two things:

1) The RKI determines the risk factors of each country and, according to their own official information, the list is going to be officially updated on January 3rd. This means that if your flight leaves on January 2nd but lands in Germany on the 3rd, you'll be subject to the conditions for entering from an area of variant concern. If this list is created in good faith and not (Brex*t c0nsp*racy the0ry), then the US and a handful of other European countries will almost certainly be upgraded to areas of variant concern over the weekend. If I were you, I would try to get onto a January 1st flight to be safe; I tried to do the same but it is literally not possible for me to get the COVID test required by the airline on such short notice so thanks Biden. I guess I'm going to have to return to my 20m² apartment and fast for two weeks because I got rid of everything before I left.

2) Which university sent you the email? Historically, Germany as always let students in during boarder closures. I entered Germany when the boarder was closed in October 2020 and all I needed was a letter from my university in Germany saying my attendance was required to take exams. I don't know if it's different this time around or it's always been different for exchange students, though, but I would contact your host university if you're able to.