it looks like that, but actually it is not.
the project / code is on the server,
when the browser starts it downloads the HTML and that code
and executes it after it finds it in the index.html <script src="sketch.js"></script>
ALL ON YOUR COMPUTER.
and in your computer RAM create something ( text picture… ) by your script
and when you want to save, it asks you where on you computer?
but FROM RAM,
nothing of this happens at the server side…
so no, saving to server is not possible, must upload later.