With macOS Sequoia, Apple is requiring users to regularly reauthorize permissions for screen recording apps, but you may not have to do it quite as often with a change that's being implemented in macOS Sequoia 15.1.
In the release notes for the sixth beta of the macOS Sequoia 15.1 update, Apple says that users aren't going to see as many popups for apps they regularly use.
Applications using our deprecated content capture technologies now have enhanced user awareness policies. Users will see fewer dialogs if they regularly use apps in which they have already acknowledged and accepted the risks.
During the macOS Sequoia beta testing process, Apple was showing permission popups for screen recording apps on a weekly basis, which people quickly got tired of. The permission setting was tweaked to show a popup only once per month prior to when macOS Sequoia launched, but now users will see fewer popups once they've given an app they use on a regular basis screen recording permissions.
The prompt that Apple shows is designed to remind users that apps are able to record screen and system audio, including sensitive information.
[App Name] is requesting to bypass the system private window picker and directly access your screen and audio. This will allow [App Name] to record your screen and system audio, including personal or sensitive information that may be visible or audible.
There is no option to remove the popup permanently, but macOS Sequoia 15.1 may make the frequency of the popup more bearable for those who use screen recording apps on a daily basis. macOS Sequoia 15.1 is expected to see a release on Monday, October 28.