What I'm trying to do is host a JSON document that will then, essentially, serve as a hosted version of json-server. I'm aware I can do something similar with My JSON Server, but I plan to move my entire architecture to GCP so want to get more familiar with it.
At first I looked into the Storage JSON API, but it seems like that's just for getting data about buckets rather than the items in the buckets itself. I created a bucket called test-json-api and added a test-data.json, but there's seemingly no way to access the data in the json file via this API.
I'm trying to keep it as simple as possible for testing purposes. In time, I'll probably use a firestore allocation, but for now I'd like to avoid all that complexity, and instead have a simple GET and a PUT/PATCH to a json file.
The Storage JSON API you are talking about are only for getting and updating the metadata and not for getting and updating the data inside the object. Objects inside the Google Cloud Storage bucket are immutable and one way to update them may be to get the object data from Google Cloud Storage bucket within the code, updating it, then uploading it again into the Google Cloud Storage bucket.
As you want to deal with JSON files you may explore using Cloud Datastore or Cloud Firestore. Also if you wish to use Firebase then you may explore Firebase Realtime Database.