I have of course tested all steps from S22 to S24, I try to avoid answering from memory.
Please have a look here:
More in detail
Open the Asset Browser and drag the lib file in it. When you double-click on the icon, the Content Browser opens, and you have a familiar view of your content as before.
I have saved in S22 a color swatch as a library.
With the Preferences> Open Preferences Folder…>> Library> Browser> User.lib found the swatches and dragged that file to the S24 Asset Browser. From there, I was able to drag it into my material.
Perhaps have a look here, scroll all the way down:
(One word is not translated Farbfelder = Color Fields.)
Besides that, perhaps you got the Color fields from the CV_Swim? (ASE files)
All the best