Appears that Rayner has played her hand well - essentially, she is signalling that there should be a contest, and if the Starmerites now block Burnham there’ll be civil war, which would legitimise a challenge.
This is a perilous moment for Starmer - he is hugely unpopular and with Labour polling 17%, a vast swathe of backbenchers can see themselves losing their seats.
For Burnham, Rayner’s support adds to his risk - if he doesn’t run, he looks weak and she looks magnanimous, but he could easily lose and then she looks even stronger as the candidate to run against Starmer.