Hi there, drubinoff. I'm here to share the report you can run to see invoices issued for a project, including whether they are paid. 

Please know that there's no direct feature to run a report that includes invoices issued for a project, but on the brighter side, we can customize and filter the Invoices and Received Payments report based on your desired criteria. 

To customize and filter reports:

1. Hover to Reports, then enter Invoices and Received Payments in the search bar.
2. In the Report period, select your preferred date range.
3. Click Customize, then pick Change columns. 
4. Tick Open Balance and A/R Paid.
5. Tap Filter, and tick all the project names you want to show in the report. 
6. Hit Run report. 

I've included a screenshot for visual reference. 
 

Moreover, you have the option to memorize the reports you've customized. This way, you won't have to do the customization process again. To learn more about what you can generate, check out this article: Reports included in your subscription. 

You can always reach out by tapping the reply button below. I'd be available to assist if you need further information on what report you can generate in QuickBooks Online.