This looks really nice, some friends didn't really like the current design of Lemmy and I think I could convince them to use it through a design like yours. Svelte really is a great tool to quickly get something working. I'm currently rewriting another site in SvelteKit as well.
About CORS / WebSocket. I'm not sure where it will be going with the WebSocket API. The main Lemmy project wants to use the WebSocket API less, as it a high performance impact on instances, and it also often seems to break in the PWA.