Well Trump has just announced that Starmer is resigning....Rumours of Starmer just quitting are gathering pace
There was no way he could go through with standing in a leadership election, it would just be humiliating for him.
And he seems to be extremely disliked from what Labour MPs say they hear locally, which makes it more difficult for him to remain and for Labour MPs to support him. I really don't know why he is disliked so much, he seems a decent enough person (aside from football allegiance choice) but he doesn't seem to have the communication skills to sell what Labour is doing.
My guess is he will set out a fairly short transition period, rather than have the process drag out all summer.