MAS-76 The issues getting worse on the 2015 15" with macOS 11 and later — point less to the design of the OS as the cause IMO — and more to the very likely case that newer AMD/Intel graphics drivers & firmware are provided with OS 11+ that render the image differently or change what graphics functionality is enabled by default.
If you look at a pixel-perfect screenshot of a modern macOS version, but on the older version that's working better for you, and it looks better than if that newer macOS version was running on the laptop itself — this would confirm the problem is the graphics drivers that are built-in to 11 and later.