So it turns out the params is passed into the Single-File Vue Component as a prop, but since IHeaderParams is an interface you can't just do the following

const defineProps( {
  'params': IHeaderParams
});

Instead, I ended up having to use this work-around to read in params and also set it to type IHeaderParams:

const props = defineProps(['params']);
const params : IHeaderParams = props.params as IHeaderParams;