Maybe I am, but I'd argue that in that case I'm depicting literally all professions as rent-seeking, as people really want to protect their income and livelihoods from infringement that would endanger them. And at that point it's probably not useful to talk about it as rent-seeking.

If AI can do literally any job more efficiently than a human, then there's no need for human labour anymore and at least to me that seems that unless we get a radical transformation of our political economy, that will not be allowed to happen. You can't just put literally everyone out of a job, capitalism just wouldn't be able to cope with it and it'd implode, most probably because of the inevitable backlash that would occur for to no one being able to afford the basic necessities of life. It would be orders of magnitude bigger than either the French or Russian revolutions.

I'm no mathematician, but if being concerned about being able to keep my employment to be able to feed myself makes me a rent-seeker, then I will wear that on my sleeve proudly, crossing my heart, hoping to die. The misery of the alternative is too great to fathom.

"Rent-Seeking" is trying to capture eternally recurring payment for something you did or acquired one time.

Mathematicians acquired their skills over long hours of study, but weren't asking to be paid just to sit around passively being smart, but to keep working on new results. It is the lost opportunity to do work they are lamenting, not the lost opportunity to sit on their laurels. So no, it doesn't sound like rent-seeking.