I think there’s a setting to enable cloud storage, so as long as you’re logged into Firefox Sync/Chrome it can be synced but has to be triggered manually to sync/merge the filter lists.
> If syncing is enabled, the data is synced to any Chrome browser that the user is logged into. If disabled, it behaves like storage.local. When the browser is offline, Chrome stores the data locally and resumes syncing when it's back online. The quota limitation is 100 KB approx, 8 KB per item. Consider using it to preserve user settings across synced browsers.
https://developer.chrome.com/docs/extensions/reference/stora...
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[1] https://developer.mozilla.org/en-US/docs/Mozilla/Add-ons/Web...