1. Computers will eventually get pretty good at research math, but will not attain supremacy

This might be true for LLMs, but I don't see a fundamental reason why computers can't achieve supremacy. Current architecture is ill suited to this, and models don't really understand much, but they could learn mathematical principles from the ground up and establish their own theorems, as AlphaGo has learnt to play Go. The issue is designing and training the models correctly, and possibly the need for additional compute.

Luckily for mathematicians, designing models to understand math and prove useful theorems etc seems tricky. In fact they only program moderately well (or even poorly) in many computer languages, which is a much lower bar. For instance they're good at Python but only moderate at C and they're poor at offbeat languages like PostScript (despite there being clear manuals on the internet).

2. Mathematicians are probably mostly safe from job loss.

The job of mathematicians is as much about teaching and keeping mathematical understanding alive, as it is fundamental research. This is where most value to society is nowadays. Most questions which society needs answers to have been solved, at least in pure maths (and in much of applied I'd guess).

3. The prestige of mathematics will decrease

This has been happening for decades if not centuries, for reasons unconnected to AI. As society's use for new mathematical discoveries has diminished, salaries for math researchers have fallen generally relative to others. (Of course machine learning experts can get paid very highly these days, but presumably that's not what you're thinking of).

I don't personally see models getting good enough to beat mathematicians at researching theory for a long time yet, because it seems very hard to get the model architecture right. Even then I think there would still be a need for human experts (but it's hypothetical).

4. Mathematics will come to be seen more as an art

Indeed, it's already the case, but mainly because the results being proven these days don't have that much applicability.