T-5: set up API-first tooling with OpenAPI spec as single source of truth

Backend: openapi-generator-maven-plugin generates Spring interfaces and DTOs
from the spec. Frontend: openapi-typescript + openapi-fetch provide type-safe
API access. Both sides get compile-time contract enforcement from a single
api.yaml file.

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

backend/src/main/resources/application.properties

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