Is it still possible to nest panels within panels within the customizer?

No, panels are not currently designed to support nesting. This has never been officially supported by core. Any solutions to implement the effect would currently involve hacks. A middle ground can be seen in widgets and nav menus, however, where you can see that controls for nav menu items and widget instances both are expandable to reveal controls. These controls, however, do not appear on separate panes like panels and sections do.

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