T-2: add multi-stage Dockerfile and SPA-serving Spring Boot config

Replace server.servlet.context-path=/api with addPathPrefix so API
endpoints stay under /api while static resources and SPA routes are
served at /. Spring Boot falls back to index.html for unknown paths
(SPA forwarding). Multi-stage Dockerfile builds frontend (Node 24)
and backend (Temurin 25) into a single 250MB JRE-alpine image with
Docker-native HEALTHCHECK.

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

backend/src/test/java/de/fete/config/WebConfigTest.java

@@ -0,0 +1,33 @@
+package de.fete.config;
+
+import static org.springframework.test.web.servlet.request.MockMvcRequestBuilders.get;
+import static org.springframework.test.web.servlet.result.MockMvcResultMatchers.jsonPath;
+import static org.springframework.test.web.servlet.result.MockMvcResultMatchers.status;
+
+import org.junit.jupiter.api.Test;
+import org.springframework.beans.factory.annotation.Autowired;
+import org.springframework.boot.test.autoconfigure.web.servlet.AutoConfigureMockMvc;
+import org.springframework.boot.test.context.SpringBootTest;
+import org.springframework.test.web.servlet.MockMvc;
+
+@SpringBootTest
+@AutoConfigureMockMvc
+class WebConfigTest {
+
+  @Autowired
+  private MockMvc mockMvc;
+
+  @Test
+  void actuatorHealthIsOutsideApiPrefix() throws Exception {
+    mockMvc.perform(get("/actuator/health"))
+        .andExpect(status().isOk())
+        .andExpect(jsonPath("$.status").value("UP"));
+  }
+
+  @Test
+  void apiPrefixNotAccessibleWithoutIt() throws Exception {
+    // /health without /api prefix should not resolve to the API endpoint
+    mockMvc.perform(get("/health"))
+        .andExpect(status().isNotFound());
+  }
+}