I heard Burnham being interviewed about various things. He's a lot like Starmer, no particular principles about anything, just vague promises about making everything wonderful. He doesn't seem to have any more concrete ideas than Starmer. I reckon he'd be OK working with Starmer and will give him a job, in fact Starmer will probably demand it in return for politely standing aside after Burnham becomes an MP.
Then Burnham and Starmer's henchmen will bang heads together behind the scenes to ensure that nobody else stands, to avoid a leadership election.
It will be like Blair's handover to Brown - reluctant but swiftly and politely dealt with.