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

backend/src/main/resources/openapi/api.yaml

@@ -0,0 +1,37 @@
+openapi: 3.1.0
+info:
+  title: fete API
+  description: Privacy-focused event announcements and RSVPs
+  version: 0.1.0
+  license:
+    name: GPL-3.0-or-later
+    identifier: GPL-3.0-or-later
+
+servers:
+  - url: /api
+
+paths:
+  /health:
+    get:
+      operationId: getHealth
+      summary: Health check
+      tags:
+        - health
+      responses:
+        "200":
+          description: Service is healthy
+          content:
+            application/json:
+              schema:
+                $ref: "#/components/schemas/HealthResponse"
+
+components:
+  schemas:
+    HealthResponse:
+      type: object
+      required:
+        - status
+      properties:
+        status:
+          type: string
+          example: UP