Some GPU come with a very aggressive fan profile. Since all modern browser use GPU to accelerate. When you scrolling up and down, the GPU and the associated VRAM actually work a bit harder than "just display something (2D idle)". In some case, it's just strong enough to trigger the fan to spin up (keep jumping above and below the "fan spin up threshold". Therefore, you will able to hear the fan on and off. In fact, if the demand is bigger, and make the fan keep spinning at a faster RPM, you may not notice it at all. But when the noise signature keep changing, it's very easy to catch your attention.
One of the easy test is browning Facebook. It's quite demanding (as a webpage), and can use lots of VRAM. Also, you can keep scroll down forever (particular useful for this test). If you can hear the fan spin up and down when browsing in Firefox. Then I am quite sure there is no solution in MacOS apart from flashing your card (with a more gentle fan profile).
Anyway, you may still try to stress the card a bit after boot to desktop. Luxmark for 10 seconds is good enough. Just in case the power control bug not just affect the PCIe & PSU fan, but also make your card unable to correctly stay at low power mode.
If you can hear the fan spin up before stress test (e.g. using Firefox), then try to stress it for few seconds and do the test again. If no more fan noise, then it means your card need something to stress it EVERYTIME after you boot to desktop. Otherwise, it won't work properly.
But if the fan still spin up and down after stress test. Then I am 99.99% sure flash it is the only way to fix it.