The notes themselves are already online anyway.
PS In reference to running AI locally: for my own (non-online) app (Calcish) I specifically waited to introduce AI until local modals become usable, as I didn't want to just add APIs and be done with it — it happened and now the app provides a choice.
Local AI in browsers is something that's Chrome working on (https://news.ycombinator.com/item?id=40834600) — I think it can already be adapted for Grug Notes use cases.