Indeed, there was an error in my code with the HTTP methods!
The following now works
GET https://management.azure.com/providers/Microsoft.Billing/billingAccounts/{billingaccount_id}/invoices
Then I get a response 200, with the field value -> documents -> URL
for a download link. Using this link in a POST yields
POST https://management.azure.com/providers/Microsoft.Billing/billingAccounts/<billingaccount_id>/invoices/<invoice_id>/download?downloadToken=<download_token>&api-version=2020-05-01
results in a 202, with a header containing Location
. A GET on this location, downloads the PDF
GET https://management.azure.com/providers/Microsoft.Billing/billingAccounts/<billingaccount_id>/invoices/<invoice_id>/operationResults/invoiceDownload_<...>?api-version=2020-05-01&t=<very_long_token>
Thanks for the quick help!