How else would you suggest full applications run in the browser. Desktop apps make use of SQLite all the time even when they are mostly server backed.
An example is that Telegram maintains a local db which stores the most recently accessed content so you can scroll through past messages and media without having to request them every time you view them.
Desktop apps use SQLite because it's the embedded structured datastore that already exists, not because they want to use SQL. If it was easy to embed, IDK, some kind of file-backed redis, I'm pretty sure a lot of apps would use that instead.
