[LudiusMaximus]

I solved it myself. Turns out that for recipes, which create usable items, the hyperlink returned by GetItem() does not match the returned id. The hyperlink is of the created item but the id is of the recipe. So when I use the returned id I am good.

TooltipDataProcessor.AddTooltipPostCall(Enum.TooltipDataType.Item, function(self)
 
  local name, link, idFromTooltip = self:GetItem()
  local idFromLink = tonumber(string_match(link, "^.-:(%d+):"))
  
  if idFromTooltip ~= idFromLink then
    print("This recipe has the id", idFromTooltip, "and creates another teaching item with the id", idFromLink)
    
    print("Tooltip of created item:")
    local tooltipLines = C_TooltipInfo.GetItemByID(idFromLink).lines
    local numLines = 1
    while tooltipLines[numLines] do
      print(numLines .. ":", tooltipLines[numLines].args[2].stringVal)
      numLines = numLines + 1
    end
  end
  
  print("Tooltip of recipe:")
  local tooltipLines = C_TooltipInfo.GetItemByID(idFromTooltip).lines
  local numLines = 1
  while tooltipLines[numLines] do
    print(numLines .. ":", tooltipLines[numLines].args[2].stringVal)
    numLines = numLines + 1
  end
 
end)