Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Having the Billing Administrator role alone does not necessarily give the user access to every billing account/billing profile. Microsoft specifically documents assigning billing-account roles to Billing Administrators.
Based on the above description of the issue this is likely cause by permissions. For this case just assign the Billing account contributor role to the existing Billing Administrator and subsequently you should be able to see the rest of the billing accounts as well as able to change billing accounts .