feat(lyra)!: 接入 Redis 并添加缓存连通性实验

- 封装缓存读写、JSON 编解码、过期时间与操作超时
- 集中组装 Redis 依赖，在测试接口验证分类缓存读写
- 更新依赖并移除原 handler 测试

BREAKING CHANGE: 配置节由 redis 改为 cache，新增 db 和 timeout 配置项

go/projects/lyra/internal/cache/cache.go

@@ -0,0 +1,68 @@
+package cache
+
+import (
+	"context"
+	"encoding/json/v2"
+	"errors"
+	"fmt"
+	"time"
+
+	"github.com/redis/go-redis/v9"
+)
+
+type Entry[T any] struct {
+	Key   string
+	Value T
+	TTL   time.Duration
+}
+
+type Cache struct {
+	client           *redis.Client
+	operationTimeout time.Duration
+}
+
+func NewCache(client *redis.Client, timeout time.Duration) *Cache {
+	return &Cache{
+		client:           client,
+		operationTimeout: timeout,
+	}
+}
+
+func (c *Cache) Get[T any](ctx context.Context, key string) (T, bool, error) {
+	var zero T
+	operationCtx, cancel := context.WithTimeout(ctx, c.operationTimeout)
+	defer cancel()
+
+	payload, err := c.client.Get(operationCtx, key).Result()
+	cancel()
+	if errors.Is(err, redis.Nil) {
+		return zero, false, nil
+	}
+	if err != nil {
+		return zero, false, fmt.Errorf("读取缓存失败：%w", err)
+	}
+	var value T
+	if err := json.Unmarshal([]byte(payload), &value); err != nil {
+		return zero, false, fmt.Errorf("缓存解码失败：%w", err)
+	}
+	return value, true, nil
+}
+
+func (c *Cache) Set[T any](ctx context.Context, entry Entry[T]) error {
+	if entry.TTL < 0 {
+		return fmt.Errorf("缓存过期时间必须大于等于零: %v", entry.TTL)
+	}
+	if err := ctx.Err(); err != nil {
+		return fmt.Errorf("写入缓存失败：%w", err)
+	}
+	payload, err := json.Marshal(entry.Value)
+	if err != nil {
+		return fmt.Errorf("缓存编码失败：%w", err)
+	}
+	operationCtx, cancel := context.WithTimeout(ctx, c.operationTimeout)
+	defer cancel()
+	if err := c.client.Set(operationCtx, entry.Key, payload, entry.TTL).Err(); err != nil {
+		return fmt.Errorf("写入缓存失败：%w", err)
+	}
+	return nil
+}