The LCD is extremely fragile. Removing the screen almost certainly will damage the display, no matter how carefully it’s removed unfortunately. You likely need a new screen.
On the cellular model the sim reader needs to be disconnected as well. It’s located just below the battery connector and has a little piece of black tape covering it.
On the cellular model be sure to disconnect the two antenna up by the front facing camera on the board as well as the sim card reader connector by the battery connector.
If your replacement screen comes with the frame you’ll need to to be sure to transfer over the other small components including the volume buttons, mics, ear speaker, and vibrating motor as well.