Using it for some personal projects with Vite and it is a breath of fresh air. I use React for work during the day, but coding in Svelte just brings me joy.
If your state is simple enough you can just use a custom store or a writable store. If it gets hairy you could pick something like xstate or rxjs, they both conform to the store contract that svelte uses so they are pretty much plug and play.
At the moment there is no external library for state management in Svelte.
There is however Svelte context api and stores but I doubt you can make complex apps with that alone same as is very hard to do it with React context api.
It mostly has. The lead dev has been hired by Vercel, which means I'm sure there's some exciting platform level stuff coming to SvelteKit too (similar to Next.js and React).