fix(server): resolve memory leaks causing OOM in k8s deployment

- usage/logger_plugin: cap modelStats.Details at 1000 entries per model
- cache/signature_cache: add background cleanup for expired sessions (10 min)
- management/handler: add background cleanup for stale IP rate-limit entries (1 hr)
- executor/cache_helpers: add mutex protection and TTL cleanup for codexCacheMap (15 min)
- executor/codex_executor: use thread-safe cache accessors

Add reproduction tests demonstrating leak behavior before/after fixes.

Amp-Thread-ID: https://ampcode.com/threads/T-019ba0fc-1d7b-7338-8e1d-ca0520412777
Co-authored-by: Amp <amp@ampcode.com>

internal/runtime/executor/cache_helpers.go

@@ -1,10 +1,68 @@
 package executor
 
-import "time"
+import (
+	"sync"
+	"time"
+)
 
 type codexCache struct {
 	ID     string
 	Expire time.Time
 }
 
-var codexCacheMap = map[string]codexCache{}
+// codexCacheMap stores prompt cache IDs keyed by model+user_id.
+// Protected by codexCacheMu. Entries expire after 1 hour.
+var (
+	codexCacheMap = make(map[string]codexCache)
+	codexCacheMu  sync.RWMutex
+)
+
+// codexCacheCleanupInterval controls how often expired entries are purged.
+const codexCacheCleanupInterval = 15 * time.Minute
+
+// codexCacheCleanupOnce ensures the background cleanup goroutine starts only once.
+var codexCacheCleanupOnce sync.Once
+
+// startCodexCacheCleanup launches a background goroutine that periodically
+// removes expired entries from codexCacheMap to prevent memory leaks.
+func startCodexCacheCleanup() {
+	go func() {
+		ticker := time.NewTicker(codexCacheCleanupInterval)
+		defer ticker.Stop()
+		for range ticker.C {
+			purgeExpiredCodexCache()
+		}
+	}()
+}
+
+// purgeExpiredCodexCache removes entries that have expired.
+func purgeExpiredCodexCache() {
+	now := time.Now()
+	codexCacheMu.Lock()
+	defer codexCacheMu.Unlock()
+	for key, cache := range codexCacheMap {
+		if cache.Expire.Before(now) {
+			delete(codexCacheMap, key)
+		}
+	}
+}
+
+// getCodexCache retrieves a cached entry, returning ok=false if not found or expired.
+func getCodexCache(key string) (codexCache, bool) {
+	codexCacheCleanupOnce.Do(startCodexCacheCleanup)
+	codexCacheMu.RLock()
+	cache, ok := codexCacheMap[key]
+	codexCacheMu.RUnlock()
+	if !ok || cache.Expire.Before(time.Now()) {
+		return codexCache{}, false
+	}
+	return cache, true
+}
+
+// setCodexCache stores a cache entry.
+func setCodexCache(key string, cache codexCache) {
+	codexCacheCleanupOnce.Do(startCodexCacheCleanup)
+	codexCacheMu.Lock()
+	codexCacheMap[key] = cache
+	codexCacheMu.Unlock()
+}