Is it possible to add windowing components to existing panels (like buttons, dropdowns, etc…) or even create custom panels? If so, are there any good existing plugins that would be good to use as an example?

No, sadly you can not create anything GUI-like other than window.show_quick_panel, window.show_input_panel and sublime.ok_cancel_dialog, sublime.message_dialog, sublime.error_message (if you even count these).

Related: Python GUI lib/module