SQLite has a system that abstracts various low-level storage operations called VFS - this is the layer that allows SQLite to be portable across different operating systems and environments: https://www.sqlite.org/vfs.html

Recently I’ve wondered how possible it would be to implement a SQLite VFS on top of IndexedDB - and, would such a VFS be competitive in speed to using IndexedDB directly? Or, would it be equivalent to use Emscripten’s existing POSIX-ish filesystem backed by IndexedDB?

An IndexedDB VFS would allow sql.js to durably persist data in the browser.

There are a few neat adjacent things that it can be used for (e.g. opening big SQLite files on disk without reading it all to memory), building something like Datasette (https://github.com/simonw/datasette) that can run queries on data hosted as static files, or for (as you suggested) using SQLite in a browser with persistence.

For that particular use case, there's a bit of complexity related to mutexes and stuff in trying to prevent simultaneous browser tabs doing write operations from corrupting the database.