Properly integrate the new Image Paste feature with the rest of the system

As of 3.6 you can go to your web browser, right click an image, copy, go to blender, image editor, image > paste and get the image into your blender instance.

From here you cannot pack the image into the blend file, even if File > External Data > Automatically Pack Resources is activated.

Other features and addons that can work with packed images or the render result cannot work with a pasted image.