fix(core): hide stale panes when switching docks in popup mode

[SaKaNa-Y]

Description

Fixed the issue where stale panes were not hidden when switching docks in popup mode, causing panel overlap.

like this:

Linked Issues

Additional context

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commit: 1fd2a7f

[SaKaNa-Y]

Some UI updates in popup mode are not applied immediately and only update after the mouse moves back into the host page. I'm not sure how many cases are affected yet, so I'll continue checking and verifying them later.