I'm wondering if this post indicates it's more than just the driver update that caused it. It could be a glitch in a GUI update for ShadowPlay itself.
The following indicates it still works if you use the Share button instead of the usual button (or the record hotkey), which means nothing is missing but that button on the GUI.
"After an update on the NVIDIA program the button to start recording had simply disappeared and appeared a new button in place "SHARE", which has an arrow next to. I clicked on that arrow and did not show any recording option. So after much searching, discovering that it was necessary to click on the name to show the functions I was looking for. So when you open the NVIDIA and display the "share" button instead of the button "shadowplayer" only you click the name "SHARE" that will appear starting the recording options, flow, diffusion, among others. Not to click the arrow next to the word "SHARE" is exactly on top of the name.
The game only starts recording when you get into a game compatible with shadowplayer and press Alt + Z, where appear the same options as when you click on the word "SHARE"."