Well no, not permanent damage. I don’t think there were ever any PCs where dropping the power could permanently damage your PC. What can happen is you screw up your data, either just your personal files or something in the OS. This can easily cause your computer to simply not boot. Depending on the issue, this can be fixed easily, or can require an entire restore/reinstall. Now modern Windows is pretty good with detecting and repairing that shit, but still, it’s not something you’d ever want to have happen.
But pushing the button isn’t a hard shutdown, that’s just how you tell the computer to go do it’s shutdown thing. That’s not a hard shutdown at all, that’s a regular vanilla shutdown.
With old shit, when hard drives had moving parts and didn’t auto park their heads, not parking before turning it off and then moving the system could absolutely crash the head destroying the disk. Even that isn’t like permanent damage to the PC, because you could simply replace the drive, but still. But we’re talking 80s and early 90s, after that the default state was parked and the drive had to move it to an unparked state.