While I've been unable to turn this off, I found a semi-functional workaround is to increase the Workbench > Hover: Delay value from 500 to 1000. I don't think I tend to use the workbench hovers very often, so the extra delay for the tooltips I want isn't too much of an irritation.

This was happening to me typically when I was selecting a tab then clicking back to the terminal. I've only just learned that you can focus the terminal by double-clicking on the tab. You can also change this behaviour to happen on single click by changing the Terminal > Integrated > Tabs: Focus Mode setting. At least this way I'm not needing to click on the terminal behind the tooltip, and can move the mouse toward the code panel. I wish I'd known the double-click shortcut earlier.