What problem/error are you having exactly?
The management api doesn’t do link resolution (which means the UI Extension SDK doesn’t either), so it might be useful to instantiate a delivery or preview api client inside your UI Extension simply to get the tree of content more easily.
For example, I built a nested category browser UI extension which displays a tree of categories to reference from another entry and I used a CDA client to get the tree of categories within my UI extension.
I hope this helps!