Definitely not. This is a bog standard MFM aka ST506 type drive, the A590 used an XT bus drive (the 8 bit variant of IDE) - very rare and not worth looking for (or SCSI of course). The drive even looks like a 5.25" drive, no way to fit it into an A590.
MFM drives can be used on an A2090(a) or an ALF controller.
PS: must've been some ancient laptop... :roll: