feat(backend): implement HTTP API, auth, chat, and admin surfaces

Expose learning, registration controls, mentor chat, realtime WebSocket, and staff administration.

backend/internal/api/util.go

@@ -0,0 +1,7 @@
+package api
+
+import "strconv"
+
+func strconvFormatInt(v int64) string {
+	return strconv.FormatInt(v, 10)
+}