Neither article is about a leadership contest. The Guardian article boils down to "Starmer is all we have to beat the Tories, so we have to go with it". No particular enthusiasm for Starmer as such.
The Guardian article is about a possible Starmer-led government. The BBC item is about Corbyn standing to be an MP.
One of those possibilities is a near-irrelevance. The other isn't.
This idea that there is no enthusiasm for Starmer is being oversold. There is enough enthusiasm for him for people to explicitly choose him in polling to demonstrate a 26 point lead over the other possible main choice.
That Starmer isn't
exactly what those being polled want is neither here nor there. Leaders rarely are exactly what people want. Not only is it inherent in a system based on compromise, but such a mythical person may not exist, at least outside of the realms of populism...and we can see where populism has taken us with both Boris Johnson and Jeremy Corbyn.