feat(sdk/typescript): Vercel AI SDK chat-persistence adapter (closes #37)

[mkorbi]

The last of the three framework adapters in #37 — after the Python LangGraph (#46) and CrewAI (#47) ones, this is the TypeScript Vercel AI SDK adapter. Unblocked now that the TS SDK (#44) is merged.

What it does

The AI SDK persists a chat as its full UIMessage[], loaded by id at the start of a request and re-saved after each turn. This maps that convention onto the kv block — one key per chat holding the JSON message array.

• New subpath export @memsidecar/client/ai (src/ext/vercel.ts): createChatStore → loadChat(id) / saveChat({chatId, messages}) (matching the AI SDK's persistence points) plus createChat / deleteChat / listChats.
• Typed to ai's UIMessage via a type-only import; ai is an optional peer dependency, so importing the base client never pulls it in (mirrors the Python memsidecar[langgraph] extra pattern).
• The client is typed against a structural { kv } subset (a full MemSidecar satisfies it), so the store unit-tests with a fake and stays decoupled.

import { MemSidecar } from "@memsidecar/client";
import { createChatStore } from "@memsidecar/client/ai";

const store = createChatStore(new MemSidecar(addr, { token }));
const chatId = await store.createChat();
const messages = await store.loadChat(chatId);
// ...stream a turn, then:
result.toUIMessageStreamResponse({ originalMessages: messages,
  onFinish: ({ messages }) => store.saveChat({ chatId, messages }) });

Verification

tsc typecheck + build clean; dist/ext/vercel.{js,d.ts} ship in npm pack; offline tests (mock kv) cover round-trip, empty/unknown chat, list/delete, and namespace isolation — all pass. (The TS SDK isn't gated by the repo's Go/buf CI, so this was verified locally.)

Closes #37. README documents the toUIMessageStreamResponse wiring.

Note: touches sdk/typescript/package.json + package-lock.json, which #55 (publish workflows) also edits — trivial rebase for whichever lands second.