There can be several reasons for why you can't see Budget Checking in your QuickBooks Online Bill, Purchase Order or Expense:
The request doesn't match the Category in the budget
The request doesn't match the Customer/Location/Class
The budget check period doesn't match
The Budget Checking setting How should a 0 planned amount on a request be handled? is not set as "Display the budget with a 0 amount", and the planned budget is 0
The budget is deactivated
The request is not On Review or On Approval