Register AGT-02 services in DI container and wire inbox triage tool

The tool registry, policy evaluator, and inbox triage assistant were
missing DI registrations, making the entire feature unresolvable at
runtime. Also registers the inbox.triage tool definition at startup
so the policy evaluator can find it.

Author: Chris0Jeky

backend/src/Taskdeck.Api/Extensions/ApplicationServiceRegistration.cs

@@ -1,5 +1,6 @@
 using Taskdeck.Api.Realtime;
 using Taskdeck.Application.Services;
+using Taskdeck.Domain.Agents;
 
 namespace Taskdeck.Api.Extensions;
 
@@ -51,6 +52,15 @@ public static IServiceCollection AddApplicationServices(this IServiceCollection
         services.AddScoped<IBoardRealtimeNotifier, CompositeBoardRealtimeNotifier>();
         services.AddSingleton<IBoardPresenceTracker, InMemoryBoardPresenceTracker>();
 
+        // Agent tool registry (singleton — populated once at startup, read concurrently)
+        var toolRegistry = new TaskdeckToolRegistry();
+        toolRegistry.RegisterTool(InboxTriageAssistant.GetToolDefinition());
+        services.AddSingleton<ITaskdeckToolRegistry>(toolRegistry);
+
+        // Agent policy evaluator and inbox triage assistant
+        services.AddScoped<IAgentPolicyEvaluator, AgentPolicyEvaluator>();
+        services.AddScoped<InboxTriageAssistant>();
+
         return services;
     }
 }