feat(infra): wire PayloadHandlerInitHostedService (AddonLifecycle + setter)

G connects PayloadHandler to the runtime — this is the activation point
after E1-E6 built the type and F registered it in DI:

- StartAsync calls MessageList.AttachPayloadHandler(_payloadHandler) to
  complete the §6.2 cycle-resolution (ctor-cycle was broken by setter,
  this is where the setter actually fires)
- StartAsync registers AddonLifecycle listener for MoveTooltip on
  PostUpdate of "ItemDetail" and "ActionDetail" addons
- StopAsync unregisters the listener
- Both Register/Unregister wrapped in Plugin.Framework.RunOnFrameworkThread
  as defensive insurance — IAddonLifecycle thread-affinity is not
  explicitly documented in Dalamud API; wrap keeps the v1.5.6 runtime
  contract intact (per spec §5-G note)

Mirrors existing IpcManagerInitHostedService / TypingIpcInitHostedService
pattern in Infrastructure/Hosting/. PluginHostFactory adds the
AddHostedService<PayloadHandlerInitHostedService>() registration.

After G, the chunked-message-render pipeline is end-to-end functional:
MessageList renders via ChunkRenderer, _handler is wired so popups fire
on click/hover, MoveTooltip repositions native item-tooltips away from
the chat window.

HellionChat/Infrastructure/Hosting/InitHostedServices.cs

@@ -1,7 +1,9 @@
+using Dalamud.Game.Addon.Lifecycle;
 using Dalamud.Plugin;
 using HellionChat.Integrations;
 using HellionChat.Ipc;
 using HellionChat.Themes;
+using HellionChat.Ui.Components;
 using Microsoft.Extensions.Hosting;
 
 namespace HellionChat.Infrastructure.Hosting;
@@ -101,3 +103,41 @@ internal sealed class FailedTellNotifierInitHostedService(FailedTellNotifier not
 
     public Task StopAsync(CancellationToken cancellationToken) => Task.CompletedTask;
 }
+
+internal sealed class PayloadHandlerInitHostedService(
+    PayloadHandler payloadHandler,
+    MessageList messageList
+) : IHostedService
+{
+    public async Task StartAsync(CancellationToken cancellationToken)
+    {
+        // §6.2 cycle-resolution: both singletons exist by the time HostedServices
+        // run, so this is the first safe point to wire the setter.
+        messageList.AttachPayloadHandler(payloadHandler);
+
+        // IAddonLifecycle thread-affinity is not explicitly documented; wrap is
+        // defensive insurance — mirrors the window-registration RunOnFrameworkThread
+        // pattern established in PluginLifecycle.cs.
+        await Plugin.Framework.RunOnFrameworkThread(() =>
+        {
+            Plugin.AddonLifecycle.RegisterListener(
+                AddonEvent.PostUpdate,
+                "ItemDetail",
+                payloadHandler.MoveTooltip
+            );
+            Plugin.AddonLifecycle.RegisterListener(
+                AddonEvent.PostUpdate,
+                "ActionDetail",
+                payloadHandler.MoveTooltip
+            );
+        });
+    }
+
+    public async Task StopAsync(CancellationToken cancellationToken)
+    {
+        await Plugin.Framework.RunOnFrameworkThread(() =>
+        {
+            Plugin.AddonLifecycle.UnregisterListener(payloadHandler.MoveTooltip);
+        });
+    }
+}