Add DynamoDB state adapter

[anatolzak]

Feature Request

Add a DynamoDB state adapter (@chat-adapter/state-dynamodb) to provide a serverless-native persistence option for the chat SDK.

Motivation

The existing state adapters (Redis, Postgres, in-memory) all require persistent server infrastructure. A DynamoDB adapter would be a natural fit for serverless deployments (AWS Lambda, Vercel) — no connection pooling, no server management, pay-per-request pricing.

Proposed Design

• Single-table design with pk/sk string keys, no GSIs
• DynamoDBDocument client for shorthand methods
• Atomic lock operations via DynamoDB conditional expressions
• Dual-layer TTL: native DynamoDB TTL for GC + app-level checks for correctness