As a ‘Billing Account User’ I logged in, navigated to ‘My Billing Account’ but I couldn’t see projects linked to that account. I have ‘My User Project’ but I am unable to change or view the billing account associated to that project.
Below is an official description of
Billing Account User from GCP:
This role has very restricted permissions, so you can grant it broadly, typically in combination with Project Creator. These two roles allow a user to create new projects linked to the billing account on which the role is granted.
You can read more at Overview of Cloud Billing access control.
So basically, you need to make your user able to access and modify the billing of project, i.e., your user account must have enough permission on the project itself. If only the role
Billing Account User is assigned and nothing else, that is not enough to configure the billing for a project.