[circonian]

They have an OnReceiveDrag, here is an example that prints the name of the inventory item or skill & sets the button texture to that item/skill:

XML:

Warning: Spoiler

<GuiXml>
  <Controls>
        <TopLevelControl name="TestAddon_Drag" clampedToScreen="true" mouseEnabled="true" movable="true" hidden="false" resizeHandleSize="12">
            <Dimensions x="64" y="64" />
            <Anchor point="CENTER" offsetX="0" offsetY="0" />
            <Controls>
                <Button name="$(parent)Button" clampedToScreen="true" mouseEnabled="true" layer="1" level="1" tier="1">
                    <AnchorFill />
                    <OnInitialized>
                        self:GetParent().btn = self
                    </OnInitialized>
                        
                    <OnReceiveDrag>
                        TestAddon.OnDragReceive(self)
                    </OnReceiveDrag>
                </Button>
    
                <Backdrop name="$(parent)BG" inherits="ZO_DefaultBackdrop"  hidden="false" alpha="1" layer="0" level="0" tier="0" >
                    <AnchorFill />
                    <OnInitialized>
                        self:GetParent().backdrop = self
                    </OnInitialized>
                </Backdrop>
                <Texture name="$(parent)Icon" clampedToScreen="true" hidden="false" >
                    <Anchor point="TOPLEFT" relativeTo="$(parent)" offsetX="4" offsetY="4"/>
                    <Anchor point="BOTTOMRIGHT" relativeTo="$(parent)" offsetX="-4" offsetY="-4"/>
                    <OnInitialized>
                        self:GetParent().icon = self
                    </OnInitialized>
                </Texture>
            </Controls>
        </TopLevelControl>
  </Controls>
</GuiXml>

Lua:

Warning: Spoiler

local MY_CURSOR_INFO = {}
 
local function OnReceiveDragInventoryItem(self)
    local bagId     = GetCursorBagId()
    local slotIndex = GetCursorSlotIndex()
    
    -- Do whatever
    local name = GetItemName(bagId, slotIndex)
    local icon = GetItemInfo(bagId, slotIndex)
 
    self:GetParent().icon:SetTexture(icon)
    d("Bag Item: "..name)
    
    -- when done with cursor item:
    ClearCursor()
    MY_CURSOR_INFO = {}
end
 
local function OnReceiveDragAction(self)
    -- Do whatever
    local name, icon = GetSkillAbilityInfo(MY_CURSOR_INFO.skillType, MY_CURSOR_INFO.lineIndex, MY_CURSOR_INFO.index)
    local msg = zo_strformat("<<1>>: <<2>>, <<3>>, <<4>>", name, MY_CURSOR_INFO.skillType, MY_CURSOR_INFO.lineIndex, MY_CURSOR_INFO.index)
 
    self:GetParent().icon:SetTexture(icon)
    d(msg)
    
    -- when done with cursor item:
    ClearCursor()
    MY_CURSOR_INFO = {}
end
    
    
function TestAddon.OnDragReceive(self)
    local cursorContentType = GetCursorContentType()
    
    if cursorContentType == MOUSE_CONTENT_INVENTORY_ITEM then
        OnReceiveDragInventoryItem(self)
        
    elseif cursorContentType == MOUSE_CONTENT_ACTION then
        OnReceiveDragAction(self)
    end
end
 
local function OnActionDragStart(control)
    if(GetCursorContentType() == MOUSE_CONTENT_EMPTY) then
        if not ZO_Skills_AbilityFailsWerewolfRequirement(control.skillType, control.lineIndex) then
            MY_CURSOR_INFO.skillType    = control.skillType
            MY_CURSOR_INFO.lineIndex    = control.lineIndex
            MY_CURSOR_INFO.index        = control.index
        end
    end
end
ZO_PreHook("ZO_Skills_AbilitySlot_OnDragStart", OnActionDragStart)

EDIT: You don't have to do it with xml. You could set the handler with lua also:

TestAddon_Drag:SetHandler("OnReceiveDrag", TestAddon.OnDragReceive)