ntfschr@ mentioned on https://chromium-review.googlesource.com/c/chromium/src/+/1376709:

As a privacy consideration, apps might want to *not* expose this to servers, so it might make sense to provide a toggle? From a technical perspective, such a toggle could be a manifest tag, or a Java API on WebSettings(Compat). (not saying there *is* a privacy concern, just advising how we might consider building that, from a technical standpoint)

As for persisting to disk, this would live somewhere under the app's data dir. I don't think we have a standard way of persisting data (for example, cookies and preferences are both persisted, and I suspect they use different formats on disk). Paul could chime in here though, if I'm mistaken.