While helping another User recently about the same issue except on a 280Hz Monitor getting the same error. Found this 5/2022 thread at another forum that states that it seems like Radeon has a Pixel Clock Cap or Limit:
It seems the Pixel Clock is capped at 240hz or below. Anything above 240Hz you will get an error. But it should be fine in Windows Settings -Display.
So you can use your Monitor's 360hz Resolution under Windows OS as long as Windows shows it being supported under Windows Settings - Graphics.
If Windows doesn't recognize that Frequency you can try using CRU (Custom Resolution Utility) which is very small and free to use.
NOTE: Not sure how reliable that thread information is until AMD Support verifies it from the other User.