Nicola Sturgeon writes (briefly) about Burnham in her book. She doesn't automatically criticise opposition party politicians. Burnham has also probably matured and grown in stature since being mayor and since she worked alongside him. She is fulsome in her praise of Alan Johnson who she seems to admire more than any other politician for his abilities and contrasts him with AB , largely because he seemed not as meticulous, thoughtful, listening and , tellingly perhaps, not as good with civil servants as Johnson was.
I know some by default may not want to to hear what she says but she has no particular reason to say anything about Burnham so it's an objective assessment.
He is in a tricky spot now himself because he certainly doesn't want to do a David Miliband and come across as person before party and entitled. He seems to eb well aware of this himself,at least.