I know you've been through a lot already, rogeraf.

Let's get this sorted out. The suggested report given by my colleague by running the Transaction Lists with splits will give us the information needed. We'll have to make sure that the Customer/Client box is also checked mark so we can easily track those expenses that are unbilled to clients.

The screenshot below will show you how reports will appear:

This report displays your both billed and unbilled transactions.

If in case you're interested in exporting your reports, you can refer to this article for the detailed steps: Export your reports to Excel from QuickBooks Online

Please tag me directly if there's anything else I can do to help. Thanks!