For anyone running into the "washed-out problem" in Unity 6.

This "problem" also exists in recent versions but I'm not sure in which specific version Unity switched their defaults. But it's related to switching the project's color space to Linear instead of Gamma (which you might have done on your own in older versions of Unity. But Unity Technologies thought it made sense to switch to Linear as their new default for new projects)
If you want to use Unity's default Linear color space:
The atlas images need to be exported with Premultiply alpha unchecked.


In Unity, the 🖼️ Texture asset of the atlas needs to have sRGB (Color texture) checked

In Unity, the 🔵 Material asset needs to have Straight Alpha Texture checked. This setting may not be necessary if you are using other shaders.

If you don't want to use the default Linear color space, just go to the project settings and change the color space to Gamma.
Note that there are reasons why you'd use either color space so... I guess that can be a discussion?
I'm posting this as a simple user-side fix for now. And to keep it apart from a separate post I'm writing.