Take a look at Michael Deacon's Twitter feed. He's a right wing hack but as well as Boris, he's currently being super critical of Nadine Dorries and also highlighting negative coverage of the government's treatment of homeless people too.
The right wing press aren't a homogeneous mass and at least some of them are very sensitive to what they perceive to be competence - something they often value above ideology, at least as long as ideology is within a certain acceptable boundary.
Starmer has what they view as competence in spades, and Corbyn didn't. It's superficial, but I think a huge portion of the public think the same way.