Add local liveness health endpoint

backend/Controllers/HealthController.cs

@@ -7,6 +7,12 @@ namespace Nexus.Api.Controllers;
 [ApiController]
 public class HealthController(IAgentRuntime runtime, HealthCheckService healthChecks) : ControllerBase
 {
+    [HttpGet("/health/live")]
+    public IResult Live()
+    {
+        return Results.Ok(new { status = "Healthy", timestamp = DateTimeOffset.UtcNow });
+    }
+
     [HttpGet("/health")]
     public async Task<IResult> Get(CancellationToken ct)
     {

compose.yaml

@@ -53,7 +53,7 @@ services:
       postgres:
         condition: service_healthy
     healthcheck:
-      test: ["CMD-SHELL", "wget --no-verbose --tries=1 --spider http://localhost:8080/health || exit 1"]
+      test: ["CMD-SHELL", "wget --no-verbose --tries=1 --spider http://localhost:8080/health/live || exit 1"]
       interval: 30s
       timeout: 10s
       retries: 3