To export the Expenses and Payments from a single Event, go the Event Budget tab and click the three dots at the top right corner of the Expenses or Payments table.
To export Budget reporting from multiple Events, go to Org Reports & Settings, then Budgets. Note that your access to Org Reports may be limited by your Permissions.
Click the three dots at the top-right corner of the Budgets table, then "Download current view (CSV)" which includes the currently applied Filters and Group Bys.
You can optionally include Expenses and Payments, along with Event totals (Planned, Actual & Paid).