No.
The only objects that could be damaged are, in order of disappearance: audio tape reels, ZIP disks, floppy disks, audio and video cassettes and recorders, analog oscilloscopes, magnetic compasses, credit cards with magnetic strip and LTO tapes.
Magnetometers (electronic compasses) in phones might suffer too, I'd avoid strong magnets nearby.
HDDs seem to be very resilient, people have tried to place magnets directly on them, and the data remained intact.
Even CRTs are not that delicate. On a very old colour TV, I placed a speaker magnet directly on the screen. That caused very strong colour and geometric distortion, and some of it remained after I removed the magnet. But it all disappeared next time it was power on, because colour CRTs always had degaussing coils (which could damage audio cassettes, ha).