It's not entirely clear what you're asking. Are you saying there is a way for Jamf Pro to enable screen recording on a managed/enrolled Mac or iPad? If so, I haven't seen this anywhere (maybe in a really old version of Casper).

Apple has been quite aggressive about not allowing us Mac Admins to programatically enable screen recording. It is a privacy concern. In fact, if you search these boards, you'll find lots of admins asking how to do this, so that end users don't have to -- this is usually for remote support programs like Webex, TeamViewer, etc.

My last understanding was that when a device is supervised, there are more options to programatically enable screensharing and recording. When a device is not supervised, it is up to the end user to manually enable these options in Security & Privacy.

Just to clarify what you're looking for is to disable the screenshot functionality? If so the restrictions payload in a configuration profile can disable those. The key you're looking for is under the Functionality tab.