refactor: rewrite backend in Go, replacing Python FastAPI

Port the FastAPI backend to Go 1.26, preserving all API functionality:
- auth (register/login/guest/logout/profile/history) with JWT + bcrypt
- scripts (list/detail) backed by embedded sample_data.json
- games (create/join/start/chat/phase/clue/vote/state/replay) + WebSocket
- rule-based NPC agent plus DeepSeek/Ollama AI backends
- SQLite persistence via modernc.org/sqlite (pure Go, no cgo)

Frontend and documents are unchanged.

backend/internal/util/timeutil.go

@@ -0,0 +1,25 @@
+package util
+
+import "time"
+
+const PyTimeLayout = "2006-01-02T15:04:05.999999"
+
+func NowStr() string {
+	return time.Now().UTC().Format(PyTimeLayout)
+}
+
+func TimeStr(t time.Time) string {
+	return t.UTC().Format(PyTimeLayout)
+}
+
+func ParseTime(s string) time.Time {
+	if s == "" {
+		return time.Now().UTC()
+	}
+	for _, layout := range []string{PyTimeLayout, "2006-01-02T15:04:05", "2006-01-02 15:04:05", time.RFC3339} {
+		if t, err := time.Parse(layout, s); err == nil {
+			return t
+		}
+	}
+	return time.Now().UTC()
+}