But I get it. Unfortunately something like this cannot be a sidecar, or at least I do not know how to make it one. It's central to your app in the way that React is.
Fortunately the category is expanding and there are several sync engines that plug in exactly how Zero does - by replicating your database. You can switch between them easily. So as long as you think you do need a sync engine you aren't that married to Zero specifically.
Here's a demo of that!