feat: NCS-37 add backcore Quarkus module skeleton

Introduces the backcore Quarkus REST module with build configuration,
application.yml, and a smoke test confirming Quarkus boots successfully.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

settings.gradle.kts

@@ -1,8 +1,23 @@
 rootProject.name = "NowChessSystems"
+
+pluginManagement {
+    val quarkusPluginVersion: String by settings
+    val quarkusPluginId: String by settings
+    repositories {
+        mavenCentral()
+        gradlePluginPortal()
+        mavenLocal()
+    }
+    plugins {
+        id(quarkusPluginId) version quarkusPluginVersion
+    }
+}
+
 include(
     "modules:core",
     "modules:api",
     "modules:io",
     "modules:rule",
     "modules:ui",
-)
+    "modules:backcore",
+)