There is multiple issues going on https://status.cloud.google.com/ I am not able to access my cloud console / login to any of my machines on GCP from cloud shell
Pity the geniuses at Google couldn't/wouldn't design their heavily replied upon APIs to keep functioning if their BILLING is broken.
You have no proof that the billing API is the underlying cause. It seems like the root issue is from something else which is effecting multiple systems.