> I can verify it with get(), but I want a debug tool for inspection
No such thing yet, AFAIK.
> Chrome's built-in devtools > Application > Storage doesn't have it (only window.localStorage).
> the "Storage Area Explorer" extension
It shows the tab's main document only.
> inspecting the manifest page, but that shows no data
> inspecting the popup page ('default_popup') but that had no data either - presumably it's a different chrome.storage.local.
It still works assuming you open it correctly with a chrome-extension:// URL and not file:// URL or
http://localhost.
chrome.storage is the same for all parts of the extension.
> try to "Inspect" my devtools page, Storage Explorer doesn't come up as an option - extensions can't run on top of a devtools panel I think.
Correct.