I keep getting a tickle in my brain that says "Smith is a stooge a la Eagle", but who for? Smith is certainly egotistic enough to believe he's a big cheese, but in reality he's a self-important nobody, who'd be the desperation shag at any office party. Is he being set up to show Chooks or Andy "Scott Tracey" Burnham in a better light?
Smith has long wanted to be leader, so as far as he's concerned this is his big chance.
As far as some others are concerned, this is no different to Eagle. Anyone with serious intentions towards the leadership who isn't of a Corbyn-lite bent would be absolutely stupid beyond measure to put themselves forward at the moment. To be sure, Tom Watson is holding off until next time (as long as next time isn't against Corbyn in any way), as I'm sure are people like Jarvis and possibly Ummuna, although I really do think we're seeing the Blairite-proper star wane now.
Despite hyperbole to the opposite effect, there aren't that many true Blairites left -- most of these 'moderates' are simply products of an individualist politics that doesn't understand the role of party and membership (perhaps doesn't want to understand it) and are scattered here there and everywhere between Blairism, Brownism, and various other non-nameable positions that you might simply just call soft-left/liberal. Certainly, it's easier to just say 'Blairite' but it's not strictly true, unless all we mean is 'the end result of Blair's experiments with the party.'
Anyway, the usual suspects who you would expect to have an eye on the leadership are biding their time. They'd be stupid to throw their hat in the ring while Corbyn is still leader. They'll wait for him to go -- however that might happen -- and then they'll make their move seemingly untainted by the unseemly business of coups and plots. Which is why we haven't heard a great deal from Creasy, Ummuna, Hunt, Jarvis, etc. And which is why, although we've heard a lot from Watson, he very quickly put to rest the idea that he might want to stand himself. Of course he's shot himself in the foot by being the bully boy with the unions -- they won't forget that.
Also, Burnham wants to be mayor of Manchester -- I don't think he'll stand for leader again unless something extraordinary happens that requires him to step up.