I’m not aware of any budgeting apps that you can feed the transactions into directly, from Monzo (I haven’t searched either though).
But if you can handle a two step process, you could feed Expenses transactions into a tool like FieldBook or Google sheets, download that data as a CSV file & then upload it into a budgeting app…@chdhurry has written some script to handle the first part of that process & shared the code here -