Obama isn't supporting Kamala not because he wants "an open contest" but because he wants to push his wife as an option. He asked Gavin Newsom to be her pick for VP but he refused and wants to wait until he is termed out of Calfornia's governorship so he can enter national stage after the trump shadow is away.
Barack also asked Bernie Sanders for support and to pressure the delegates at the DNC but since he is an independent but democrat aligned senator <he caucuses with them> he refused but since his apprentices aka Ilhan, AOC, and the like have come out supporting Kamala I think he will throw his weight behind her.
I mentioned in another post minority house leader Hakeem Jefferies was one of the organisers of the Biden pushout campaign and he and his senior backer Pelosi succeeded. However they're waiting to see who will come out on top or who will be most beneficial to their platforms. Their small group of reps and senators might have what it takes to swing the ball in favour of either camp and supposedly negoations are going on between them and the Harris4 Prez camp.