I have consulted with the Apple Platform Deployment and the Device Management Documentation but am unable to find the setting that allows/controls applications with access to Privacy & Security > Screen Recording.
In MacOS Ventura, the user must toggle on/allow applications requesting access to Screen Recording.
Is there not a payload that can be delivered to set these applications with permissions to Screen Recording across our devices?
This behaviour is by design, Apple does not allow an MDM to control this setting directly.
However, you can use PPPC utility (https://github.com/jamf/PPPC-Utility) to send a mdm profile to allow non admins to allow screen recording to desired apps without needing admin rights to approve it, but users will still need to manually approve it the first time.
Confirming what Brandon said below: Apple believes that user privacy is a right, and that even on machines they do not own, they must consent to allow the screen recording function, as well as the activation of the camera and microphone, by each app that wants to access these key resources. Apple does accept feedback requests, and I would strongly recommend that you tell them why they should allow user privacy to be compromised on a corporate device. You can file a feedback request with Feedback Assistant, present on any Mac.