Not enough information. When you say "app folders list" are you referring to the app drawer (where you go when swiping u up from the homescreen), or do you mean an actual folder with apps in it? There's no problem at all dragging a shortcut from the homescreen to a n app folder, even if its on a different screen. Moving a shortcut from an app folder to the homescreen is also np. But moving something into the app drawer via a method other than installing as new is not possible. However, many 3rd party launchers allow you to directly create a shortcut wherever you want, even web shortcuts.
Yes, referring to the app drawer (where you go when swiping u up from the home screen). URL short cut is on the home screen (cannot drag it to app drawer. Likewise, my app folder from the drawer cannot be dragged to the home screen. Unsuccessful. (perhaps this is a permissions issue? - needing to be turned on first?) - new phone
Welcome to Android Central! As Mr. Lucky said, most stock launchers don't support folders in the App Drawer. I think Samsung's One UI allows it, but the Pixel Launcher doesn't. I don't have a Motorola phone, but they tend to make their launcher to be very similar to the Pixel Launcher. (I do have a Lenovo tablet, which is the same company, and it's not possible there either.) And folders in the App Drawer would typically only be for app icons, not URL shortcuts.