Is it possible to copy 2GB of data to the clipboard? If it's an image or something I'd expect the clipboard to contain a reference to the image or some such. How do clipboard managers handle this?

Yes. It contains a reference to the image in the source application.

When you paste, X or Wayland lets the source application communicate with the destination application to send the image over.

You’ll likely always have a very simple clipboard manager that stores a single copy of the clipboard so you don’t rely on the source application staying alive.

Clipboard managers are free to store the clipboard anywhere.