There is no need to set up a new account or a new budget.
It also doesn't matter if the account is Active in Chart of Accounts. In the tools of Budgeting and financial reporting, the word "active" means In Use. Not Make Inactive for purposes of Seeing it, or not, in the COA and in dropdowns.
If you Budget it as 0, it should show. It also matters if this is a Parent Level account or not, with subaccounts.
And in Reporting, go to the Customize, Display tab, bottom right, and if there is an Advanced Button, click on it. Here is where you control selecting NonZero or All, or only Rows/Columns with values.