Hi,
I'm also experiencing the same issue with my Nitro+ RX 5700 XT. I can hear the weird buzzing sound (most likely coil whine), even when I just move mouse cursor around the desktop screen. Obviously it also happens in games, even under relatively low gpu load, and even when fps is capped to 60 (says a lot about build quality of this GPU...).
Regarding fans starting randomly in idle...have you checked memory temps. of your GPU? Many people (particularly those who use 75hz and 144hz monitors) are experiencing (driver?) issue with 5700 XT memory clocks being stuck and causing high temps when idle. This obviously compromises the fan stop function, because fans are turning on/off all the time due to idle memory clock temperature fluctuations (we could say that 5700 XT never idles on certain monitors at certain refresh rates, particularly 75/144hz).
In my case GPU temperature is constantly well above 60°C in idle (which is definitely not normal) when I use my monitor's native refresh rate (75hz), it normalizes when I set 60hz refresh rate.