[Feat][Router] Support Redis as Response API storage backend

[Xunzhuo]

Summary

Add Redis as a storage backend for the Response API to enable fast, distributed conversation storage.

Background

PR #802 introduced Response API support with a pluggable storage interface. Currently, only the in-memory store is implemented. Redis would provide:

• Persistence: Survive router restarts with RDB/AOF
• Distribution: Share state across multiple router instances
• Native TTL: Built-in expiration for conversation cleanup
• High performance: Sub-millisecond read/write latency

Implementation Tasks

• Implement RedisStore in pkg/responsestore/redis_store.go
• Design Redis key schema for responses and conversations
• Implement CRUD operations with Redis commands
• Add connection pooling and cluster support
• Leverage Redis TTL for automatic expiration
• Add configuration options in RedisStoreConfig
• Add unit tests for Redis store
• Add integration tests with Redis
• Update documentation

Configuration Example

response_api:
  enabled: true
  store_backend: "redis"
  ttl_seconds: 86400
  redis:
    address: "localhost:6379"
    password: ""
    db: 0
    key_prefix: "sr:response:"

Key Schema Design

sr:response:{response_id}     -> JSON blob of StoredResponse
sr:conversation:{conv_id}     -> JSON blob of StoredConversation
sr:chain:{response_id}        -> List of response IDs in chain

Related

• Parent PR: [Feat][Memory] Add OpenAI Response API support #802
• Interface defined in: pkg/responsestore/interface.go