All the permission grants are summarized in system preferences. Much more elegant to go do your own audit than have to respond to nag screens.
The nag screens are an inferior Windows security feature (think UAC) no doubt manifested as a result of The Bozo Explosion which Jobs managed to fend off for about a decade or so.
I really hate how every year I have to hope macOS won't introduce annoying new features (this annoying nagging screen), break compatibility with existing third-party apps (Intune VPN was broken for months after the release of Sonoma) or just remove existing functionality entirely altogether (subpixel aliasing was removed a few years ago resulting in awful font rendering on non-retina displays).
How can I justify spending an extraordinary amount of money on a MacBook Pro when the operating system introduces breaking changes _every year_? And on top of that, I can't even choose to run my own operating system? Very annoying.
But that's also you performing a positive action to start the (presumably time-limited) recording which is different from something in the background passively recording your screen over a long period (Bartender, etc.)
(I do not like the permission prompts but I understand where they're coming from)
If Apple wants to record your screen they don't need to use Quick Time Player to do it. They can bake it into the firmware.
If you don't trust Apple not to randomly record with Quick Time Player, you shouldn't be using macOS.
I actually think UAC on Windows has this done more clearly and is harder to go around. Wonder how that would work if it was extended for more granular permissions that apps can trigger on demand.