Is there a built-in class to do the conversion from a string to those common types?
For example, to convert "1,2,3,4" to a Thickness or "#00AABBCC" to a Brush.
No. There are no built-in from-string-converters for Thickness or Brush in UWP.
But here's how you can create a StringToSolidColorBrushConverter.
And here's the source code of .NET's System.Windows.ThicknessConverter. Though, it works only in .NET Framework, you can take the converter algorithm from the FromString(..) method.
Old post, but anyone looking for this, you can use
(Thickness)XamlBindingHelper.ConvertValue(typeof(Thickness), value)
Not just for thickness, but for lots of types. This is also working in WinUI3