[Ketho]

It's undocumented but you can just use GameTooltip.SetRecipeResultItem, instead of getting the Item Id for in GameTooltip.SetItemByID

function TradeSkillDetailsMixin:OnResultMouseEnter(resultButton)
    if self.selectedRecipeID then
        GameTooltip:SetOwner(resultButton, "ANCHOR_RIGHT");
        GameTooltip:SetRecipeResultItem(self.selectedRecipeID);
        CursorUpdate(resultButton);
    end
    
    resultButton.UpdateTooltip = resultButton.UpdateTooltip or function(owner) self:OnResultMouseEnter(owner); end;
end

This can be shortened to this

TradeSkillFrame:HookScript("OnHide", function()
    f:Hide()
end)

TradeSkillFrame:HookScript("OnHide", f.Hide)

Haven't tested your addon, but is the OnHide hook actually needed if you can just parent your tooltip to the TradeSkillFrame?

local f = CreateFrame("GameTooltip", "ProfessionItemtooltip", TradeSkillFrame, "GameTooltipTemplate")