It works: client service + server service + utility service to know server uri when app is running

HttpClientSetupService.cs

@@ -0,0 +1,50 @@
+using Microsoft.AspNetCore.Hosting.Server;
+using Microsoft.AspNetCore.Hosting.Server.Features;
+
+namespace Sandbox;
+
+public class HttpClientSetupService(
+    HttpClient httpClient,
+    IServer server,
+    IHostApplicationLifetime applicationLifetime)
+    : BackgroundService
+{
+    private readonly HttpClient _httpClient = httpClient ?? throw new ArgumentNullException(nameof(httpClient));
+    private readonly IServer _server = server ?? throw new ArgumentNullException(nameof(server));
+    private readonly IHostApplicationLifetime _applicationLifetime = applicationLifetime ?? throw new ArgumentNullException(nameof(applicationLifetime));
+
+    protected override Task ExecuteAsync(CancellationToken stoppingToken)
+    {
+        var applicationStartedToken = _applicationLifetime.ApplicationStarted;
+        if (applicationStartedToken.IsCancellationRequested)
+        {
+            ConfigureHttpClient();
+        }
+        else
+        {
+            applicationStartedToken.Register(ConfigureHttpClient);
+        }
+
+        return Task.CompletedTask;
+    }
+
+    private void ConfigureHttpClient()
+    {
+        var serverAddresses = _server.Features.Get<IServerAddressesFeature>();
+        var address = serverAddresses.Addresses.FirstOrDefault();
+        if (address == null)
+        {
+            // Default ASP.NET Core Kestrel endpoint
+            address = "http://localhost:5000";
+        }
+        else
+        {
+            address = address.Replace("*", "localhost", StringComparison.Ordinal);
+            address = address.Replace("+", "localhost", StringComparison.Ordinal);
+            address = address.Replace("[::]", "localhost", StringComparison.Ordinal);
+        }
+
+        var baseUri = new Uri(address);
+        _httpClient.BaseAddress = baseUri;
+    }
+}