How to get reference via API to an external folder shared with the App User?

I am working on an integration with a client where we use the API to automatically upload files to a folder they have shared.  I was unable to accept their custom TOS on my Service Account, so I created an App User and accepted the TOS and Collaboration there.  I am trying to access the shared folder, but I am unable to find any way to get a reference to it in the API.  I am using the "as user" behavior so that I can access things as the App User since that seems to be required in order for it to find things under the App User.

The folder is also shared with my user account, and I used that to get a shared link, but I get a basic 404 response from the API with no extra details when I try to look up that shared link (which has a custom box.com subdomain) using the latest version of the Java API Library.  I have also tried grabbing the folder ID that I see in my web view and using that to get the folder with the API, but it says the item d_134030315624 doesn't exist, even though there was no "d_" in what I passed in, and the Java API Library doesn't look like it would add that either.

What is the proper way to get a reference via the API to a folder shared with an App User created via the API? Nothing I've tried seems to work, and I'm completely stuck.

Also, if using the "as user" with an App User to access the shared folder is an issue, how can I accept a custom TOS with the Service Account? It says the user with that ID doesn't exist when I try to create the User Status entry. Or is there another way to handle this?

Thank you for any help you can provide.