Add ApiFactory test helper + /health sanity test

backend.tests/HealthTests.cs

@@ -0,0 +1,19 @@
+using System.Net;
+using FluentAssertions;
+using Xunit;
+
+namespace backend.tests;
+
+public class HealthTests(ApiFactory factory) : IClassFixture<ApiFactory>
+{
+    private readonly ApiFactory _factory = factory;
+
+    [Fact]
+    public async Task Health_returns_ok()
+    {
+        var client = _factory.CreateClient();
+        var res = await client.GetAsync("/health");
+        res.StatusCode.Should().Be(HttpStatusCode.OK);
+        (await res.Content.ReadAsStringAsync()).Should().Contain("\"ok\":true");
+    }
+}