feat: add Prometheus metrics for API

PluralKit.API/Program.cs

@@ -1,4 +1,6 @@
+using App.Metrics;
 using App.Metrics.AspNetCore;
+using App.Metrics.Formatters.Prometheus;
 
 using Autofac.Extensions.DependencyInjection;
 
@@ -10,8 +12,15 @@ namespace PluralKit.API;
 
 public class Program
 {
+    public static IMetricsRoot _metrics { get; set; }
+
     public static async Task Main(string[] args)
     {
+        _metrics = AppMetrics.CreateDefaultBuilder()
+            .OutputMetrics.AsPrometheusPlainText()
+            .OutputMetrics.AsPrometheusProtobuf()
+            .Build();
+
         InitUtils.InitStatic();
         await BuildInfoService.LoadVersion();
         var host = CreateHostBuilder(args).Build();
@@ -22,7 +31,18 @@ public class Program
 
     public static IHostBuilder CreateHostBuilder(string[] args) =>
         Host.CreateDefaultBuilder(args)
-            .UseMetrics()
+            .ConfigureMetrics(_metrics)
+            .UseMetricsWebTracking()
+            .UseMetricsEndpoints()
+            .UseMetrics(
+            options =>
+            {
+                options.EndpointOptions = endpointsOptions =>
+                {
+                    endpointsOptions.MetricsTextEndpointOutputFormatter = _metrics.OutputMetricsFormatters.OfType<MetricsPrometheusTextOutputFormatter>().First();
+                    endpointsOptions.MetricsEndpointOutputFormatter = _metrics.OutputMetricsFormatters.OfType<MetricsPrometheusProtobufOutputFormatter>().First();
+                };
+            })
             .UseServiceProviderFactory(new AutofacServiceProviderFactory())
             .UseSerilog()
             .ConfigureWebHostDefaults(whb => whb