mirza
I'm using hdmi on a dongle
I used a Type-C to HDMI adapter a while ago (Belkin, if I recall correctly) and experienced eye strain. Replacing it with a Satechi hub resolved the issue. This may not be directly applicable to your situation, but testing a different adapter is recommended.
30 Hz refresh rate results in perceptible stutter during mouse movement and scrolling, which increases visual fatigue and can contribute to headaches.
A USB-C to DisplayPort cable (or hub with DisplayPort output) would provide 4K at 60 Hz via DisplayPort Alt Mode, eliminating signal conversion. This alone may resolve part of the issue.
Also, for some reason app automatically goes back to 10 bit after sleep.
I saw in BetterDisplay there is a protection option to prevent your settings from being overwritten by the OS - maybe that will solve your problem.
For me, the most comfortable macOS on a 6bit+FRC monitor is Sonoma 14.1.2. I tried installing Sonoma 14.5. On Sonoma 14.5, the desktop wallpaper looks like it's been through heavy sharpening. And my eyes started to get tired a little faster. Sequoia is unusable on this monitor. Perhaps, this is again not your case. But the OS rendering subsystem was rewritten, and maybe what they added is causing you problems even on a true 8-bit monitor. The same goes for Windows 10 - it's completely comfortable on a true 8-bit monitor, but Windows 11 is not. The rendering is slightly different.
I used a BenQ BL2711U with Mac for about 6 years until its matrix died. It was comfortable. Although sometimes they can change not only the matrices but also, for example, the scaler, etc.