Does the synchronization work on a zip file loaded from Add-ons -> Tools for all add-ons -> Install add-on from file...?

I do a basic browser.local.sync sync test:

let monster = {
  name: "Kraken",
  tentacles: true,
  eyeCount: 10,
};

let kitten = {
  name: "Moggy",
  tentacles: false,
  eyeCount: 2,
};

browser.storage.sync.set({ kitten, monster });

and on the second profile:

await browser.storage.local.get("kitten");

but nothing happens, get("kitten") returns nothing.

QUESTIONS:

1. Does the synchronization work on a zip file loaded from Add-ons -> Tools for all add-ons -> Install add-on from file...?
   I have in manifest.json applications.gecko.id, as needed.
2. If not, what do I need to do to TEST the synchronization work?

API https://developer.mozilla.org/en-US/docs/Mozilla/Add-ons/WebExtensions/API/storage/sync