AFAICT, there's no reliable method in Chrome due to
https://crbug.com/40281264.
When it's fixed, you'll compare window.screenX to (await chrome.windows.getCurrent()).left inside the side panel.
For now though you'll have to obtain window.screenX from a content script running in any tab of this window.
Another workaround is to use event.screenX in a listener for mouseover event that's triggered by the user, which is not guaranteed to occur at all.