feat(payload-handler): wire MoveTooltip (E6 completes PayloadHandler)

E6 closes out the PayloadHandler resurrection. MoveTooltip handles the
cross-viewport AddonLifecycle tooltip-repositioning logic — reads
MainWindow.LastViewport/LastWindowPos/LastWindowSize (from A1) to filter
events and reposition the native item tooltip away from the chat window.

Whole method marked `public unsafe void` per spec §4.2 (matches v1.5.6
exactly — avoids per-read unsafe-block scoping).

LogWarning added on the unexpected-AddonArgs early-out branch (wires
_logger into real use, prevents CS0414 unused-field warning).

PayloadHandler is now feature-complete. F registers it in DI; G wires
the AddonLifecycle.RegisterListener for MoveTooltip from a HostedService;
H adds MessageList.AttachPayloadHandler setter-injection.

HellionChat/PayloadHandler.cs

@@ -1,7 +1,10 @@
 using System.Linq;
 using System.Numerics;
 using Dalamud.Bindings.ImGui;
+using Dalamud.Game.Addon.Lifecycle;
+using Dalamud.Game.Addon.Lifecycle.AddonArgTypes;
 using Dalamud.Game.ClientState.Objects.SubKinds;
+using Dalamud.Game.Config;
 using Dalamud.Game.Text;
 using Dalamud.Game.Text.SeStringHandling;
 using Dalamud.Game.Text.SeStringHandling.Payloads;
@@ -12,6 +15,7 @@ using Dalamud.Interface.Utility;
 using Dalamud.Interface.Utility.Raii;
 using Dalamud.Utility;
 using FFXIVClientStructs.FFXIV.Client.UI;
+using FFXIVClientStructs.FFXIV.Component.GUI;
 using HellionChat.Code;
 using HellionChat.Resources;
 using HellionChat.Themes;
@@ -564,6 +568,104 @@ internal sealed class PayloadHandler
         }
     }
 
+    public unsafe void MoveTooltip(AddonEvent type, AddonArgs args)
+    {
+        if (args == null)
+        {
+            _logger.LogWarning(
+                "MoveTooltip received unexpected AddonArgs type: {ArgsType}",
+                args?.GetType().Name ?? "<null>"
+            );
+            return;
+        }
+
+        // Only move if the user has the "Next to Cursor" option selected
+        if (
+            !Plugin.GameConfig.TryGet(UiControlOption.DetailTrackingType, out uint selected)
+            || selected != 0
+        )
+            return;
+
+        if (_mainWindow.LastViewport != ImGuiHelpers.MainViewport.Handle)
+            return;
+
+        var atk = args.Addon;
+        if (atk.IsNull)
+            return;
+
+        var atkBase = (AtkUnitBase*)atk.Address;
+        if (atkBase->WindowNode == null)
+            return;
+
+        if (!atkBase->IsVisible)
+            return;
+
+        var component = atkBase->WindowNode->AtkResNode;
+        var atkPos = new Vector2(component.ScreenX, component.ScreenY);
+        var atkSize = new Vector2(
+            component.GetWidth() * component.ScaleX,
+            component.GetHeight() * component.GetScaleY()
+        );
+
+        var chatRect = new MathUtil.Rectangle(
+            _mainWindow.LastWindowPos,
+            _mainWindow.LastWindowSize
+        );
+        var addonRect = new MathUtil.Rectangle(atkPos, atkSize);
+
+        if (!chatRect.HasOverlap(addonRect))
+            return;
+
+        var viewportSize = ImGuiHelpers.MainViewport.Size;
+        var isLeft = chatRect.SizeX < viewportSize.X / 2;
+        var isTop = chatRect.SizeY < viewportSize.Y / 2;
+
+        var mousePos = ImGui.GetMousePos();
+
+        // addon spawned left of mouse cursor
+        if (addonRect.X < mousePos.X)
+        {
+            if (isLeft)
+                addonRect.X = (short)mousePos.X + 5;
+        }
+        else
+        {
+            if (!isLeft)
+                addonRect.X = Math.Max(0, (short)mousePos.X - 5 - addonRect.Width);
+        }
+
+        if (!chatRect.HasOverlap(addonRect))
+        {
+            atkBase->SetPosition((short)addonRect.X, (short)addonRect.Y);
+            return;
+        }
+
+        // addon spawned above mouse cursor
+        if (addonRect.Y < mousePos.Y)
+        {
+            if (isTop)
+                addonRect.Y = (short)mousePos.Y + 5;
+        }
+        else
+        {
+            if (!isTop)
+                addonRect.Y = Math.Max(0, (short)mousePos.Y - 5 - addonRect.Height); // prevent it going below 0
+        }
+
+        if (!chatRect.HasOverlap(addonRect))
+        {
+            atkBase->SetPosition((short)addonRect.X, (short)addonRect.Y);
+            return;
+        }
+
+        // Spawning right/bottom of mouse cursor didn't solve the overlap, so we spawn it next to the chat
+        var x = isLeft ? chatRect.SizeX : _mainWindow.LastWindowPos.X - atkSize.X;
+        var y = Math.Clamp(chatRect.SizeY - atkSize.Y, 0, float.MaxValue);
+        y -= isTop ? 0 : Plugin.Config.TooltipOffset; // offset to prevent cut-off on the bottom
+
+        atkBase->SetPosition((short)x, (short)y);
+    }
+
     private const float MaxInlineIconSize = 32f;
 
     private static void InlineIcon(IDalamudTextureWrap icon)