I have an ST-10 that had the exact same issue with an ST-10 I bought used. I heard that high-piched noise immediately after plugging it in. Previous owner claimed not to hear it, so I recorded the output into a scope and verified 2 bands of noise at 8kHz and 14.5kHz. Had to send it to TDSS (authorized repair) to get both amp modules replaced. The unit was out of warranty, so it cost me $450. Good news is that I just got the unit back a few days ago and it's now dead silent and sounds great.
In short, you're not hearing things and unfortunately your unit is defective. Bob (great guy) at TDSS said the amp modules have been revised and suspects the older units were prone to this issue.
Feel free to reach out with any questions, I've spent the last couple months tracking down this issue, so happy to help.