The MPs wanted Cleverly anyway but they shit the bed trying to engineer an easy opponent for him in the final two. He's now said he's not going to join the shadow cabinet, so while Badenoch has to deal with all the struggles of being LOTO, Cleverly will be on the backbenches, giving speeches to constituency parties, improving his reputation, sounding like some sort of experienced elder statesman to contrast with Badenoch.
A VONC to put Cleverly in charge seems very likely unless Starmer's polling numbers really tank over the next few years.
The goal here is that it's famously difficult for third parties to get an appropriate measure of media attention in the UK. The newspapers are highly partisan, and the TV news interprets the 'balance' requirement to mean they can just give the government view and the main opposition view on every issue (unless the government and main opposition happen to agree - which is why the Lib Dems got a fair hearing in the media on Iraq in the early 2000s).
So third parties need to have a gimmick to trick the media into giving them airtime, which then allows them to talk about their issues. Charles Kennedy did it but being entertaining on chatshows and HIGNFY; Nigel Farage does it by being outrageous and offensive; and Ed Davey has worked out that he can do it through stunts.