In the object's material, you should be able to add either a Color Attribute Node or an Attribute Node, pick the attribute you want to use, and use it in your material in any way you want.
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/itkR2NHj.jpg)
The Color Attribute node only works with "color attributes", whereas the Attribute node works with any type of attribute (E.G. from geonodes). Because the Color Attribute node only works with color attributes, it is able to give you a drop-down list of available color attributes in the current object, whereas the Attribute Node requires searching your attributes in the Properties Editor:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/JphYav2C.jpg)
Any of these nodes work and do the job, use whichever you feel more comfortable with.
But remember that, since it's a material, you will be able to see these only in Material Preview or Rendered viewport shadings.