After adding the geometry node (Realize Instances):
My shading:
That seems a bit confusing, but before you Realize Instances, each sprinkle is treated as a separate object - all duplicates which cannot be edited independently, but each is an individual instance.
After Realize Instances, these instances become real meshes and therefore they can be edited independently - however, they are no longer individual instance objects with individual indices which can get random values assigned to them. The whole thing is now one object, but consisting of separate meshes unconnected to each other - so called islands.
And here is a solution: to use random colors on those mesh islands, in the material you have to switch the Object Info node with a Geometry node and use the Random Per Island output. Just be aware that the random colors are not distributed the same way they were before on the instances.
Another method would be to assign random values to each instance before realizing them and store the values in a named attribute. This way after realizing, all vertices of one mesh island carry the stored random value of the instance which they come from originally.
To do this, plug the Instances output into a Store Named Attribute node (which then is plugged into whatever followed the Instance On Points), set it to Float and Instance and plug a Random Value node with Min/Max 0/1 into the Values input. Then give it a name, I used "randID" here for example.
This way you can use an Attribute node in the Shader Editor, enter the name you gave it in Geometry Nodes (make sure to spell it correctly) and use these random values for the color ramp. Since each vertex of a former instance has the same value, this works like the Random Per Island.
Of course the random distribution is different from the other ones before as well, however this method comes with an advantage over the other ones: if you don't like the color distribution, you can change the Seed in the Random Value node until you're satisfied with the result.