Phase 1: Wire up OpenTelemetry in Budget.Api

Adds OTel packages (Extensions.Hosting, Instrumentation.AspNetCore/Http/EFCore,
Exporter.OTLP) and configures logging + tracing in Program.cs. Endpoint is
intentionally left unset in code — read from OTEL_EXPORTER_OTLP_ENDPOINT at runtime.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/Budget.Api/Program.cs

@@ -10,9 +10,27 @@ using Microsoft.EntityFrameworkCore;
 using Microsoft.Extensions.Diagnostics.HealthChecks;
 using Microsoft.Extensions.Options;
 using Microsoft.IdentityModel.Tokens;
+using OpenTelemetry.Resources;
+using OpenTelemetry.Trace;
 
 var builder = WebApplication.CreateBuilder(args);
 
+builder.Logging.AddOpenTelemetry(logging =>
+{
+    logging.IncludeFormattedMessage = true;
+    logging.IncludeScopes = true;
+});
+
+builder.Services.AddOpenTelemetry()
+    .ConfigureResource(resource => resource
+        .AddService(serviceName: "budget", serviceVersion: "1.0.0"))
+    .WithLogging()
+    .WithTracing(tracing => tracing
+        .AddAspNetCoreInstrumentation()
+        .AddHttpClientInstrumentation()
+        .AddEntityFrameworkCoreInstrumentation()
+        .AddOtlpExporter());
+
 var connStr = builder.Configuration.GetConnectionString("DefaultConnection")
     ?? $"Host={builder.Configuration["POSTGRES_HOST"] ?? "localhost"};" +
        $"Port={builder.Configuration["POSTGRES_PORT"] ?? "5432"};" +