feat(api-docs): generate OpenAPI components/schemas from Go structs

A new emit_jsonschema.go walks the same allow-listed structs as the zod/types/examples emitters and writes generated/schemas.ts (SCHEMAS). build-openapi mounts it under components.schemas and points each typed response obj at a $ref instead of an untyped {} blob, so Swagger renders real models and openapi-generator can emit clients.

Also add a vitest guard that safeParses every EXAMPLES entry against its generated zod schema, reviving the previously unused generated/zod.ts and catching drift between the example and schema emitters.

frontend/src/test/generated-examples.test.ts

@@ -0,0 +1,30 @@
+import { describe, it, expect } from 'vitest';
+import type { ZodType } from 'zod';
+
+import { EXAMPLES } from '@/generated/examples';
+import * as zodSchemas from '@/generated/zod';
+
+const registry = zodSchemas as unknown as Record<string, ZodType>;
+const names = Object.keys(EXAMPLES);
+
+describe('generated response examples', () => {
+  it('has at least one example to validate', () => {
+    expect(names.length).toBeGreaterThan(0);
+  });
+
+  it('pairs every example with a generated zod schema', () => {
+    const missing = names.filter((name) => typeof registry[`${name}Schema`]?.safeParse !== 'function');
+    expect(missing).toEqual([]);
+  });
+
+  it.each(names)('EXAMPLES.%s satisfies its generated zod schema', (name) => {
+    const schema = registry[`${name}Schema`];
+    const result = schema.safeParse(EXAMPLES[name]);
+    if (!result.success) {
+      throw new Error(
+        `EXAMPLES.${name} does not match ${name}Schema:\n${JSON.stringify(result.error.issues, null, 2)}`,
+      );
+    }
+    expect(result.success).toBe(true);
+  });
+});