You're absolutely right - unfortunately this has now been going on for 5 years and it doesn't seem to be a situation that Starmer is capable of fixing. In his defence, I'm not convinced anyone is. I'm increasingly starting to think it just isn't going to happen for Labour, in general.
There isn't actually that much common ground between the left and the centre anymore. If we had a proper electoral system this wouldn't be a problem, but under FPTP, it is. Maybe the way to heal this would be for Starmer to promise PR as the reward for the left falling into line. It would mean the end of Labour governing with a majority ever again if they won power that final time, but it would also mean the end of the Tories.