Stream widget chat responses (token streaming)

[rahulsainlll]

The per-product widget chat (apps/dashboard/app/api/widget/[publicKey]/chat/route.ts) waits for the full LLM reply before returning, so the user stares at nothing for ~2s. This is the biggest perceived-latency problem.

Goal

Stream tokens so text appears live (first token < ~1s), like ChatGPT/Fin.

Scope

• Change the chat route to return a streamed response (ReadableStream / SSE) instead of buffering the full reply.
• Update the Studio preview (features/products/test-preview-panel.tsx) and the embed widget (public/embed.js) to consume the stream and render incrementally.
• Plain-text replies stream; the confirm-action ({reply, action}) case can stay non-streamed for v1.

Acceptance

• First token visible in well under 1s on a warm route.
• Streaming works in both the Studio preview and the embedded widget.
• No regression to the confirm-action flow.