I appreciate you for coming back to the thread and clarifying your issue about the ability to select UNIT or HOUR in QuickBooks. I'll ensure you can see the option you want on the Invoice page by following the troubleshooting steps below.

QuickBooks Online's workflow has recently been updated. With this, selecting UNIT or HOUR when creating or updating an invoice is only available on the new layout. It could be that you have switched back to the old one, which is why the UNIT or HOUR is missing on your end.

I suggest Clicking the Try the new invoices option at the upper right corner beside the Gear icon. This way, you're able to view the new interface. I added screenshots below for visual reference.

Lastly, you may refer to this article if you need help viewing all the status of your sales transactions like open and paid invoices: View sales transactions.

Please know that you can always get back to this thread if you have any other clarifications or questions about managing your invoice in QBO. I'm always around to help, KMDezine Studio. Have a great day!