He already has a work permit to work for Saints. One that even lets him be the interim manager! Why would he need a new permit for a promotion within the same company? The system would be flooded with paperwork if every internal promotion required a new work permit.
That list is clearly nonsense. QPR don't even have a combined 49 players in their 1st team and under 21s, let alone all of them playing for the first team this season.