Introduce a `feature-sync`

[grigoryk]

Depends on #1375. Related to #1320.

Once we have a common "syncable" interface that different stores implement, we can define something like a feature-sync which is configurable with a list of Syncables and provides common functionality like scheduling (#1320), some kind of error handling (#1374), updating whatever Sync UI we'll have, etc.

┆Issue is synchronized with this Jira Task