Thanks for the detailed follow-up. Between your steps and the video, I think I have figured out what's going on.
I wasn't able to reproduce the visual glitch here (I tried your steps on a ContainerControl with both the published Studio and the current dev build), but your description pinpointed a genuine bug: the tooltip on the "…" (Choose system symbol) button can still appear over the main window while the symbol picker window is open, and that lingering tooltip popup is what flickers over the dialog as the mouse moves across it.
The cause sits in the UI framework Studio is built on: when a dialog is shown, it disables the window that opened it only at the native level, so the managed tooltip service still treats the "…" button as hoverable while the picker is open. In most configurations nothing visible comes of it (I think the effect depends on hover timing and on the dialog not covering the button) which is why it's so hard to reproduce elsewhere.
The fix is essentially your suggested workaround, built into the product: when the symbol picker opens, Studio now closes the chooser button's tooltip and keeps it from appearing until the dialog closes. It behaves normally again afterwards.
This is tracked as Objo Feedback bug #1515 and will be in the next release.