feat(llm): add LLM call recording with admin panel integration

- llm.Adapter: SetCallLogger hook for recording every API call
- llm.CallLogger: ring-buffer with Recent+Stats for admin API
- main.go: wire DeepSeek adapter to CallLogger
- Fix: single CallLogger instance for both recording and display
- Metrics: model name, duration, success/fail, tokens
- All 16 packages pass

backend/internal/logger/global.go

@@ -0,0 +1,53 @@
+package logger
+
+import (
+	"fmt"
+	"io"
+	"os"
+)
+
+// L is the global logger instance. Configure via Init().
+var L = New(os.Stderr, LevelInfo, "text")
+
+// Init configures the global logger.
+func Init(level Level, format string) {
+	L = New(os.Stderr, level, format)
+}
+
+// InitNop sets the global logger to discard all output.
+func InitNop() {
+	L = New(io.Discard, LevelDebug, "text")
+}
+
+// G returns the global logger.
+func G() *Logger { return L }
+
+// --- Global convenience methods ---
+
+func Debug(msg string, args ...any) { L.Debug(msg, args...) }
+func Info(msg string, args ...any)  { L.Info(msg, args...) }
+func Warn(msg string, args ...any)  { L.Warn(msg, args...) }
+func Error(msg string, args ...any) { L.Error(msg, args...) }
+
+func Debugf(format string, args ...any) {
+	L.Debug(fmt.Sprintf(format, args...))
+}
+func Infof(format string, args ...any) {
+	L.Info(fmt.Sprintf(format, args...))
+}
+func Warnf(format string, args ...any) {
+	L.Warn(fmt.Sprintf(format, args...))
+}
+func Errorf(format string, args ...any) {
+	L.Error(fmt.Sprintf(format, args...))
+}
+
+func Fatalf(format string, args ...any) {
+	L.Error(fmt.Sprintf(format, args...))
+	os.Exit(1)
+}
+
+func Fatal(msg string, args ...any) {
+	L.Error(msg, args...)
+	os.Exit(1)
+}