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Just for comparison, you can buy a 28 Tesla magnet that is stable over long times. Well, it's part of a 1.2 GHz NMR spectrometer, but I suspect it's the strongest magnet of that kind you can buy off the shelf.

These comparisons are often not quite fair and compare different things. The conversion to press releases tends to remove all nuance beyond "strong magnet".

It's remarkable that it's so hard to create high magnetic fields. 35 T is only 35 times higher than what's in a regular loudspeaker or brushless motor. The electric field possible in a lab must be much more than 35x what's in consumer devices.
I think the key point is they did it with a superconductor. My understanding is that while superconductors have zero resistance, there's still a limit to how much power you can dump into them before superconductivity breaks down.