Not SQL, but https://pouchdb.com/ looks like a better version of this.
Also not SQL, IndexedDB [0] Seems like a well-supported [1] document database built into the browser would beat LocalStorage in almost every way. That's what I've found in my experience at least.
Maybe SQL just isn't the right tool on either the frontend or the backend?
[0] https://developer.mozilla.org/en-US/docs/Web/API/IndexedDB_A... [1] https://caniuse.com/indexeddb