MSI X870E Carbon WIFI (rbar enabled), Ryzen 7 9800X3D, RTX 4090 Gaming OC (drivers 566.36), 64GB DDR5 6000 CL26.
Out of curiosity, I checked if I have the screen flickering bug after enabling FSR3. I tested with HAGS off and HAGS on, and in both cases I don’t have any screen flickering.
Since you have an NVIDIA graphics card, I’m wondering why you’re using FSR3 instead of NVIDIA DLSS in the game settings?
EDIT
I forced the bug on my setup – screen flickering occurs when FSR3 is enabled and NVIDIA DLSS is selected in the Anti-aliasing settings.
WORKAROUND: instead of NVIDIA DLSS, choose AMD FSR3 for Anti-a liasing as shown in the screenshot I added before editing.