feat: wire up swagger-jsdoc dynamic spec, delete static openapi.json

- Create src/swagger.ts config module for swagger-jsdoc
- Add GET /openapi.json dynamic route (generated from @openapi annotations)
- Delete static public/openapi.json (was drifting from code)
- Add @openapi annotation for deprecated /v1/signup/free in index.ts
- Import swaggerSpec into index.ts
- All 12 endpoints now code-driven: demo/html, demo/markdown, convert/html,
  convert/markdown, convert/url, templates, templates/{id}/render,
  recover, recover/verify, billing/checkout, signup/free, health

dist/routes/health.js

@@ -6,6 +6,56 @@ const require = createRequire(import.meta.url);
 const { version: APP_VERSION } = require("../../package.json");
 export const healthRouter = Router();
 const HEALTH_CHECK_TIMEOUT_MS = 3000;
+/**
+ * @openapi
+ * /health:
+ *   get:
+ *     tags: [System]
+ *     summary: Health check
+ *     description: Returns service health status including database connectivity and browser pool stats.
+ *     responses:
+ *       200:
+ *         description: Service is healthy
+ *         content:
+ *           application/json:
+ *             schema:
+ *               type: object
+ *               properties:
+ *                 status:
+ *                   type: string
+ *                   enum: [ok, degraded]
+ *                 version:
+ *                   type: string
+ *                   example: '0.4.0'
+ *                 database:
+ *                   type: object
+ *                   properties:
+ *                     status:
+ *                       type: string
+ *                       enum: [ok, error]
+ *                     version:
+ *                       type: string
+ *                       example: 'PostgreSQL 17.4'
+ *                 pool:
+ *                   type: object
+ *                   properties:
+ *                     size:
+ *                       type: integer
+ *                     active:
+ *                       type: integer
+ *                     available:
+ *                       type: integer
+ *                     queueDepth:
+ *                       type: integer
+ *                     pdfCount:
+ *                       type: integer
+ *                     restarting:
+ *                       type: boolean
+ *                     uptimeSeconds:
+ *                       type: integer
+ *       503:
+ *         description: Service is degraded (database issue)
+ */
 healthRouter.get("/", async (_req, res) => {
     const poolStats = getPoolStats();
     let databaseStatus;