Добавьте файлы проекта.

Telegrator.Hosting.Web/Components/ITelegramBotWebHost.cs

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+using Telegrator.Hosting.Components;
+
+namespace Telegrator.Hosting.Web.Components
+{
+    public interface ITelegramBotWebHost : ITelegramBotHost//, IEndpointRouteBuilder
+    {
+
+    }
+}

Telegrator.Hosting.Web/Polling/HostedUpdateWebhooker.cs

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+using Microsoft.Extensions.Hosting;
+using Microsoft.Extensions.Options;
+using Telegram.Bot;
+using Telegrator.Hosting.Web.Components;
+using Telegrator.MadiatorCore;
+
+namespace Telegrator.Hosting.Web.Polling
+{
+    public class HostedUpdateWebhooker : IHostedService
+    {
+        private readonly ITelegramBotWebHost _botHost;
+        private readonly ITelegramBotClient _botClient;
+        private readonly IUpdateRouter _updateRouter;
+        private readonly TelegramBotWebOptions _options;
+
+        public HostedUpdateWebhooker(ITelegramBotWebHost botHost, ITelegramBotClient botClient, IUpdateRouter updateRouter, IOptions<TelegramBotWebOptions> options)
+        {
+            if (string.IsNullOrEmpty(options.Value.WebhookUri))
+                throw new ArgumentNullException(nameof(options), "Option \"WebhookUrl\" must be set to subscribe for update recieving");
+
+            if (string.IsNullOrEmpty(options.Value.WebhookPattern))
+                throw new ArgumentNullException(nameof(options), "Option \"WebhookPattern\" must be set to subscribe for update recieving");
+
+            _botHost = botHost;
+            _botClient = botClient;
+            _updateRouter = updateRouter;
+            _options = options.Value;
+        }
+
+        public Task StartAsync(CancellationToken cancellationToken)
+        {
+            _botClient.SetWebhook(
+                url: _options.WebhookUri,
+                maxConnections: _options.MaxConnections,
+                allowedUpdates: _botHost.UpdateRouter.HandlersProvider.AllowedTypes,
+                dropPendingUpdates: _options.DropPendingUpdates,
+                cancellationToken: cancellationToken);
+
+            //botHost.MapGet(_options.WebhookPattern, async (Update update) => await _updateRouter.HandleUpdateAsync(_botClient, update, cancellationToken));
+            return Task.CompletedTask;
+        }
+
+        public Task StopAsync(CancellationToken cancellationToken)
+        {
+            _botClient.DeleteWebhook(_options.DropPendingUpdates, cancellationToken);
+            return Task.CompletedTask;
+        }
+    }
+}

Telegrator.Hosting.Web/TelegramBotWebHost.cs

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+using Telegrator.Hosting.Components;
+using Microsoft.AspNetCore.Routing;
+
+namespace Telegrator.Hosting.Web
+{
+    public class TelegramBotWebHost //: ITelegramBotWebHost
+    {
+
+    }
+}

Telegrator.Hosting.Web/TelegramBotWebHostBuilder.cs

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+using Telegrator.Hosting.Components;
+using Telegrator.Hosting.Web.Components;
+
+namespace Telegrator.Hosting.Web
+{
+    public class TelegramBotWebHostBuilder //: ITelegramBotHostBuilder
+    {
+
+    }
+}

Telegrator.Hosting.Web/TelegramBotWebOptions.cs

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+using Telegrator.Configuration;
+
+namespace Telegrator.Hosting.Web
+{
+    public class TelegramBotWebOptions : TelegramBotOptions
+    {
+        /// <summary>
+        /// Gets or sets uri for webhook update receiving
+        /// </summary>
+        public required string WebhookUri { get; set; }
+
+        public required string WebhookPattern { get; set; }
+
+        public int MaxConnections { get; set; }
+
+        public bool DropPendingUpdates { get; set; }
+    }
+}

Telegrator.Hosting.Web/Telegrator.Hosting.Web.csproj

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+<Project Sdk="Microsoft.NET.Sdk">
+
+  <PropertyGroup>
+    <TargetFramework>net8.0</TargetFramework>
+    <ImplicitUsings>enable</ImplicitUsings>
+    <Nullable>enable</Nullable>
+  </PropertyGroup>
+
+  <ItemGroup>
+    <ProjectReference Include="..\Telegrator.Hosting\Telegrator.Hosting.csproj" />
+  </ItemGroup>
+
+  <ItemGroup>
+	<PackageReference Include="Microsoft.AspNetCore.Routing" Version="2.3.0" />
+  </ItemGroup>
+</Project>

Telegrator.Hosting.Web/TypesExtensions.cs

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+using Microsoft.Extensions.DependencyInjection;
+using Microsoft.Extensions.Options;
+using Telegram.Bot;
+using Telegrator.Hosting.Web.Polling;
+
+namespace Telegrator.Hosting.Web
+{
+    public static class ServicesCollectionExtensions
+    {
+        public static IServiceCollection AddTelegramWebhook(this IServiceCollection services)
+        {
+            services.AddHttpClient<ITelegramBotClient>("tgwebhook").RemoveAllLoggers().AddTypedClient(TypedTelegramBotClientFactory);
+            services.AddHostedService<HostedUpdateWebhooker>();
+            return services;
+        }
+
+        private static ITelegramBotClient TypedTelegramBotClientFactory(HttpClient httpClient, IServiceProvider provider)
+            => new TelegramBotClient(provider.GetRequiredService<IOptions<TelegramBotClientOptions>>().Value, httpClient);
+    }
+}