Replace manual health endpoint with Spring Boot Actuator

Remove the hand-rolled HealthController and use spring-boot-starter-actuator
instead. Only the health endpoint is exposed, with no detail leakage.

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

backend/src/main/resources/application.properties

@@ -1 +1,4 @@
 spring.application.name=fete
+
+management.endpoints.web.exposure.include=health
+management.endpoint.health.show-details=never