I wasn't able to reproduce this, and then I was... and now I've forgotten how. 😅
My best guess is that you're entering into a state where there's confusion regarding which window has focus. If you either single-click anywhere in / on the window, or alt-tab to Orion, this shouldn't happen.
I think technically the bug here is actually that the search suggestions are being presented at all. The best change for UX is likely to alter the code so that the search suggestions are shown when either the search bar or the search suggestions themselves are hovered-over. Though I'm not familiar with VitePress; perhaps that's an upstream bug?