We've spend the last couple of years building a local-first end-to-end encrypted multiplayer notes app (Thymer). We also explored running sqlite in the browser but ultimately concluded that we didn't really sqlite or a real database at all in the browser.
What does a document system need? A few simple indexes that track links and backlinks, mentions, and hashtags. You’re broadcasting change notifications anyway (for reactive DOM updates), so updating the indexes for those manually isn’t much extra work. You apply updates eagerly and then notify other users so they can apply the same updates, with some rules to guarantee that all users end up with the same state regardless of the order in which they receive the updates. But a relational database doesn’t help with any of this. Document systems tend to be versioned, so every user action turns into another entry in a transaction log. Even queries like “last Monday’s version of my document” don’t map naturally to SQL. You can query for transactions in a given time period, but unless you have snapshots, you’re still forced to re-apply transactions all the way from t=0 if you want to re-create the document state at a given date.