I'm the maintainer of the linked website.
This morning, a mysterious user named "ranksunbounded" submitted the linked curve, which has rank at least thirty. This breaks the previous record of 29 found by Elkies and Klagsbrun in 2024.
Nobody knows whether it is possible to achieve arbitrarily high ranks.
ranksunbounded has added a comment on the curve: "it was Claude, with Levent Alpöge and Ava Howell!"
I'm a research mathematician, and to me the biggest surprise is that the user didn't identify themselves or (yet) try to claim credit for their work.
Within academia, it is to your definite advantage to have your name associated with breakthroughs, for obvious reasons. Outside academia I don't have firsthand experience, but I'd have to imagine the same holds.