Sidebar's bottom scrollbar briefly appears when an annotation is created

Investigate why creating an annotations causes the sidebar's bottom scrollbar to briefly appear as seen in this screen recording:

[bottom-scroll-blink.webm](https://github.com/hypothesis/client/assets/2719332/f8c99c94-b23b-4e34-bafd-7cf2b5e39133)

We need to verify if it happens while the save is in progress or only briefly after the save completes, and also, what is getting added to the DOM that causes that.