Can I send all Zoho billing emails to a dedicated, internal Accounting address?
All billing related emails will go to the super admin user by default.
There is no way to send them to a separate email address such as accounting@..., without changing the super admin email address.
The only workarounds would be to create a new user, with the required accounting email, on all apps, and make them super user and move you to admin user; but this will add a user license cost to the likes of CRM and Support, for example. This has license cost impact of course.
The other option, if you are concerned about Accounts receiving the license payment emails automatically to update accounting records, might be to create a simple email forwarder based on a rule like:
From address =
payments@zohocorp.com
... and have that forwarded automatically to an Accounting team.