test: add initial Cypress e2e test infrastructure

Smoke tests for verifying Cypress runs, plus basic API tests
for health and sessions endpoints.

cypress/e2e/api/health.cy.js

@@ -0,0 +1,30 @@
+/// <reference types="cypress" />
+
+describe('Session Manager API', () => {
+    describe('Health Check', () => {
+        it('should respond to the health endpoint', () => {
+            cy.request({
+                method: 'GET',
+                url: '/api/health',
+                failOnStatusCode: false,
+            }).then((response) => {
+                // The endpoint should exist and return a response
+                expect(response.status).to.be.oneOf([200, 503]);
+                expect(response.body).to.be.an('object');
+            });
+        });
+    });
+
+    describe('Sessions API', () => {
+        it('should list sessions', () => {
+            cy.request({
+                method: 'GET',
+                url: '/api/sessions',
+                failOnStatusCode: false,
+            }).then((response) => {
+                expect(response.status).to.eq(200);
+                expect(response.body).to.be.an('object');
+            });
+        });
+    });
+});