Budget is one of Finance's listed submodules, and it appears in the permission matrix alongside Invoices, Bills & Payments, Journals, Accounts, and Credit Notes. It has no working screens in this version of OCTO Ops — there's no way to create, view, or manage a budget anywhere in the application yet, whatever permissions are granted for it.
If you're looking for financial records to work with today, see Finance for what is available: Invoices, Bills & Payments, Journals, Accounts, and Credit Notes. This page will be updated once Budget has screens to document.