The attribute can be read using WorkItemAttributes.FILED_AGAINST. See  https://jazz.net/wiki/bin/view/Main/AttributeCustomization#Accessing_built_in_attributes_of.

I would suggest to read the value and look at it. It should look like /<level1>/<level2> e.g. /JKE/BRN. 

You can definitely do this, and you're almost correct, but you can't use the name directly.

Each Category has a name but it also has a unique ID, and it's this ID that you must return. This code snippet shows how to set the Filed Against by looking up the ID based on the name. If for some reason the type doesn't match a Category name, you should just return the current value of the attribute

dojo.provide("com.example.ValueProvider");

dojo.require("com.ibm.team.workitem.api.common.WorkItemAttributes");

(function() {
  const WorkItemAttributes = com.ibm.team.workitem.api.common.WorkItemAttributes;

  dojo.declare("com.example.ValueProvider", null, {

    getValue: function(attribute, workItem, configuration) {
      const catList = << the array of objects in the form of {name, id} >>;

        const wiType = workItem.getValue(WorkItemAttributes.TYPE).toUpperCase();
        const categoryId = catList.find((item) => item.name === wiType).id;
        return categoryId ? categoryId : workItem.getValue(attribute);
  });
})();

You will need to populate the array of Categories with objects containing the category name and their unique ID. There are various ways to do this, but I assume you won't have many different Work Item types (and therefore not many Categories) so the simplest way would be to just put in console.log() calls in some code that prints out the value as you change the Filed Against field

console.log(workItem.getValue(WorkItemAttributes.FILED_AGAINST));