My query: is it even possible for a power issue to cause 2k+ bad sectors on a HDD?
No, this is not possible.
When there's a power outage, we talk about sudden loss of power. This means, the computer will not be able to continue what it was doing. For a harddisk, this means that at worst, it cannot complete a write operation it was doing at that time which results in one or more files being corrupted depending if more than one files are being written to at the same time.
Even though the file is corrupted, it does not cause for bad sectors to happen.
A powerspike is another form of power failure which results in delivering more power in a short time than is good for the device. This kind of problem will damage chips but not damage platters on a harddisk, although it could do damage to an SSD. It would however also do damage to other system components.
If something creates a strong electric magnetic pulse, that pulse could cause a powerloss, but could also cause the magnetic field of platters to give bad sectors. It would however damage a lot more than just your HDD.
So it is very likely the HDD is already bad, because usage is one way to get bad sectors. In any case, it is time to replace the disk.