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/main/java/de/fete/config/WebConfig.java

@@ -0,0 +1,40 @@
+package de.fete.config;
+
+import java.io.IOException;
+import org.springframework.context.annotation.Configuration;
+import org.springframework.core.io.ClassPathResource;
+import org.springframework.core.io.Resource;
+import org.springframework.web.bind.annotation.RestController;
+import org.springframework.web.servlet.config.annotation.PathMatchConfigurer;
+import org.springframework.web.servlet.config.annotation.ResourceHandlerRegistry;
+import org.springframework.web.servlet.config.annotation.WebMvcConfigurer;
+import org.springframework.web.servlet.resource.PathResourceResolver;
+
+/** Configures API path prefix and SPA static resource serving. */
+@Configuration
+public class WebConfig implements WebMvcConfigurer {
+
+  @Override
+  public void configurePathMatch(PathMatchConfigurer configurer) {
+    configurer.addPathPrefix("/api", c -> c.isAnnotationPresent(RestController.class));
+  }
+
+  @Override
+  public void addResourceHandlers(ResourceHandlerRegistry registry) {
+    registry.addResourceHandler("/**")
+        .addResourceLocations("classpath:/static/")
+        .resourceChain(true)
+        .addResolver(new PathResourceResolver() {
+          @Override
+          protected Resource getResource(String resourcePath,
+              Resource location) throws IOException {
+            Resource requested = location.createRelative(resourcePath);
+            if (requested.exists() && requested.isReadable()) {
+              return requested;
+            }
+            Resource index = new ClassPathResource("/static/index.html");
+            return (index.exists() && index.isReadable()) ? index : null;
+          }
+        });
+  }
+}

backend/src/main/resources/application.properties

@@ -1,5 +1,4 @@
 spring.application.name=fete
-server.servlet.context-path=/api
 
 management.endpoints.web.exposure.include=health
 management.endpoint.health.show-details=never