src/routes/+page.svelte wires the thread with AISDKChat() from @assistant-ui/ai-sdk: the AI SDK chat runs as the threads scope of the assistant client, no React host required. Edit, reload, and branch switching come with it.
src/routes/api/chat/+server.ts runs streamText over convertToModelMessages and returns the AI SDK UI message stream, exactly like the Next.js templates; the default AssistantChatTransport posts the UIMessage array to /api/chat.
src/routes/+layout.ts disables SSR. provideAui creates the runtime client in component init, so rendering on the server would build a throwaway runtime per request for a page that is entirely client-driven.
React is a small runtime dependency of the AI SDK integration: @assistant-ui/tap installs its hook dispatcher while the chat resource renders, so useChat's React hook calls route to tap and React never renders anything.
Messages render as plain text. @assistant-ui/svelte has no markdown renderer yet.

Run

cp .env.example .env   # set OPENAI_API_KEY
pnpm install
pnpm dev

pnpm install runs svelte-kit sync, which generates the .svelte-kit/ directory that tsconfig.json extends.