As the other commenter points out, the ui-react (and in turn ui-react-dom) modules are optional so you can run it with full ReactDom, with abstract React (eg React Native), or without React at all.
The way to do that would be to listen to data changes (eg addCellListener) and in the listener just manipulate the DOM directly. Probably a pretty slick approach, performance-wise.
For SQLite, a variety of flavors are supported including things like ElectricSQL, Turso, and PowerSync - which all let you sync back to a server. You might also consider running a ‘client’ on a server that can listen to changes coming through web sockets and persist itself to server storage - but I haven’t written that pattern up yet.
Hopefully you’ll get a chance to try it out in the meantime though!
The way I understood it, this is similar to Firebase? Though Firefox is server side, not client side. So I would have to check out a more fully fledged example to compare them.